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2-local derivations on algebras of matrix-valued functions on a compactum

2-local derivations on algebras of matrix-valued functions on a compactum

Ayupov Shavkat Abdullayevich, Arzikulov Farhodjon Nematjonovich

Статья научная

The present paper is devoted to 2-local derivations. In 1997, P. Semrl introduced the notion of 2-local derivations and described 2-local derivations on the algebra B(H) of all bounded linear operators on the infinite-dimensional separable Hilbert space H. After this, a number of paper were devoted to 2-local maps on different types of rings, algebras, Banach algebras and Banach spaces. A similar description for the finite-dimensional case appeared later in the paper of S. O. Kim and J. S. Kim. Y. Lin and T. Wong described 2-local derivations on matrix algebras over a finite-dimensional division ring. Sh. A. Ayupov and K. K. Kudaybergenov suggested a new technique and have generalized the above mentioned results for arbitrary Hilbert spaces. Namely they considered 2-local derivations on the algebra B(H) of all linear bounded operators on an arbitrary Hilbert space H and proved that every 2-local derivation on B(H) is a derivation. Then there appeared several papers dealing with 2-local derivations on associative algebras. In the present paper 2-lo\-cal derivations on various algebras of infinite dimensional matrix-valued functions on a compactum are described. We develop an algebraic approach to investigation of derivations and \mbox{2-local} derivations on algebras of infinite dimensional matrix-valued functions on a compactum and prove that every such 2-local derivation is a derivation. As the main result of the paper it is established that every \mbox{2-local} derivation on a ∗-algebra C(Q,Mn(F)) or C(Q,Nn(F)), where Q is a compactum, Mn(F) is the ∗-algebra of infinite dimensional matrices over complex numbers (real numbers or quaternoins) defined in section 1, Nn(F) is the ∗-subalgebra of Mn(F) defined in section 2, is a derivation. Also we explain that the method developed in the paper can be applied to Jordan and Lie algebras of infinite dimensional matrix-valued functions on a compactum.

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A Beckenbach - Dresher type inequality in uniformly complete f-algebras

A Beckenbach - Dresher type inequality in uniformly complete f-algebras

Kusraev Anatoly G.

Статья научная

The Beckenbah-Dresher type inequality in uniformly complete f-algebras

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A biographical note about Safak Alpay

A biographical note about Safak Alpay

Персоналии

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A by-proxy talk on Alexandrov's contribution

A by-proxy talk on Alexandrov's contribution

Kutateladze Semen Samsonovich

Статья научная

This talk presents the unpublished articles by O. A. Ladyzhenskaya, Yu. G. Reshetnyak, and V. A. Zalgaller concerning the nomination of A. D. Alexandrov for the Wolf Prize in 1995.

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A caccioppoli type inequality

A caccioppoli type inequality

Alborova Mira Soslanovna

Статья научная

A Caccioppoli type inequality for solutions of the quasi-elliptic equations is established.

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A characterization of order bounded disjointness preserving bilinear operators

A characterization of order bounded disjointness preserving bilinear operators

Kusraev Anatoly Georgievich, Kutateladze Semen Samsonovich

Статья научная

The paper is aimed to characterize order bounded disjointness preserving bilinear operators in terms of their -spaces. To this end the Boolean valued analysis approach is employed.

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A note on weakly \Aleph_1-separable P-groups

A note on weakly \Aleph_1-separable P-groups

Danchev peteR. V.

Статья научная

It is well-known by Hill-Griffith that there exist \aleph_1-separable $p$-primary groups which are not direct sums of cycles. A problem of challenging interest, mainly due to Hill (Rocky Mount. J. Math., 1971), is under what extra circumstances on the group structure this holds untrue, that is every \aleph_1-separable p-group is a direct sum of cyclic groups. We prove here that any weakly \aleph_1-separable p-group of cardinality not exceeding \aleph_1 is quasi-complete precisely when it is a bounded direct sum of cycles, thus partly answering the posed question in the affirmative.

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A numerical method for the solution of fifth order boundary value problem in ordinary differential equations

A numerical method for the solution of fifth order boundary value problem in ordinary differential equations

Pandey Pramod Kumar

Статья научная

In this article we have proposed a technique for solving the fifth order boundary value problem as a coupled pair of boundary value problems. We have considered fifth order boundary value problem in ordinary differential equation for the development of the numerical technique. There are many techniques for the numerical solution of the problem considered in this article. Thus we considered the application of the finite difference method for the numerical solution of the problem. In this article we transformed fifth order differential problem into system of differential equations of lower order namely one and four. We discretized the system of differential equations into considered domain of the problem. Thus we got a system of algebraic equations. For the numerical solution of the problem, we have the system of algebraic equations. The solution of the algebraic equations is an approximate solution of the problem considered. Moreover we get numerical approximation of first and second derivative as a byproduct of the proposed method. We have shown that proposed method is convergent and order of accuracy of the proposed method is at lease quadratic. The numerical results obtained in computational experiment on the test problems approve the efficiency and accuracy of the method.

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A priori estimate result for an inverse problem of transport theory

A priori estimate result for an inverse problem of transport theory

Lahrech Samir

Статья научная

We establish a priori estimate result for an inverse problem of transport theory. We refer to [1], where some existence and uniqueness results are proved.

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A study on a class of $p$-valent functions associated with generalized hypergeometric functions

A study on a class of $p$-valent functions associated with generalized hypergeometric functions

El-Yagubi Entisar, Darus Maslina

Статья научная

In this paper, we study and introduce the majorization properties of a new class of analytic $p$-valent functions of complex order defined by the generalized hypergeometric function. Some known consequences of our main result will be given. Moreover, we investigate the coefficient estimates for this class.

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Abraham Robinson (1918-1974)

Abraham Robinson (1918-1974)

Kutateladze Semen Samsonovich

Персоналии

This is a short biographical sketch and tribute to Abraham Robinson on the 95th anniversary of his birth.

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An EOQ model with time-dependent increasing demand under JIT philosophy for a distributor/agent

An EOQ model with time-dependent increasing demand under JIT philosophy for a distributor/agent

Sana Shib Sankar

Статья научная

This article generalizes an EOQ model for a distributor/agent with Just-in-Time (JIT) philosophy. It is assumed that the demand of seasonal goods is an increasing function of time. The optimality condition of the associated objective function is derived analytically. Also, the model is illustrated with the numerical examples.

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An almost f-algebra multiplication extends from a majorizing sublattice

An almost f-algebra multiplication extends from a majorizing sublattice

Kusraev Anatoly Georgievich

Статья научная

It is proved that an almost f-algebra multiplication defined on a majorizing sublattice of a Dedekind complete vector lattice can be extended to the whole vector lattice.

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Arnold is gone (obituary)

Arnold is gone (obituary)

Персоналии

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Artin's theorem for $f$-rings

Artin's theorem for $f$-rings

Kusraev Anatoly Georgievich

Статья научная

The main result states that each positive polynomial $p$ in $N$ variables with coefficients in a unital Archimedean $f$-ring $K$ is representable as a sum of squares of rational functions over the complete ring of quotients of $K$ provided that $p$ is positive on the real closure of $K$. This is proved by means of Boolean valued interpretation of Artin's famous theorem which answers Hilbert's 17th problem affirmatively.

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Atomicity in injective banach lattices

Atomicity in injective banach lattices

Kusraev Anatoly Georgievich

Статья научная

This note is aimed to examine a Boolean valued interpretation of the concept of atomic Banach lattice and to give a complete description of the corresponding class of injective Banach lattices.

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Banach - Steinhaus type theorem in locally convex spaces for \sigma-locally lipschitzian convex processes

Banach - Steinhaus type theorem in locally convex spaces for \sigma-locally lipschitzian convex processes

Lahrech S., Jaddar A., Hlal J., Ouahab A., Mbarki A.

Статья научная

The main purpose of this paper is to generalize the Banach--Steinhaus theorem in locally convex spaces for \sigma-locally Lipschitzian operators established by S. Lahrech in [1] to \sigma-locally Lipschitzian convex processes.

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Banach lattices of continuous sections

Banach lattices of continuous sections

Kusraev Anatoly G., Tabuev Soslan N.

Статья научная

The aim of this note is to outline some application of ample continuous Banach bundles to the theory of Banach lattices.

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Banach lattices with topologically full centre

Banach lattices with topologically full centre

Wickstead Anthony W.

Статья научная

After some general background discussion on the notion of a topologically full centre in a Banach lattice, we study two problems in which it has featured. In 1988 Orhon showed that if the centre is topologically full then it is also a maximal abelian algebra of bounded operators and asked if the converse is true. We give a short proof of his result and a counterexample to the converse. After noting that every non scalar central operator has a hyperinvariant band, we show that any hyperinvariant subspace must be an order ideal, provided the centre is topologically full and conclude with a counterexample to this in a general vector lattice setting.

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Bernstein - Nikolskii type inequality in Lorentz spaces and related topics

Bernstein - Nikolskii type inequality in Lorentz spaces and related topics

Bang Ha Huy, Cong Nguyen Minh

Статья научная

In this paper we study the Bernstein - Nikolskii type inequality, the inverse Bernstein theorem and some properties of functions and their spectrum in Lorentz spaces L^{p,q}(\R^n).

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