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Generalized Derivations and Norm Equality in Normed Ideals

Barraa, Mohamed (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.We compare the norm of a generalized derivation on a Hilbert space with the norm of its restrictions to Schatten norm ideals.

Generalized derivations associated with Hochschild 2-cocycles on some algebras

Jiankui Li, Jiren Zhou (2010)

Czechoslovak Mathematical Journal

We investigate a new type of generalized derivations associated with Hochschild 2-cocycles which was introduced by A. Nakajima. We show that every generalized Jordan derivation of this type from CSL algebras or von Neumann algebras into themselves is a generalized derivation under some reasonable conditions. We also study generalized derivable mappings at zero point associated with Hochschild 2-cocycles on CSL algebras.

Generalized derivations on Lie ideals in prime rings

Basudeb Dhara, Sukhendu Kar, Sachhidananda Mondal (2015)

Czechoslovak Mathematical Journal

Let R be a prime ring with its Utumi ring of quotients U and extended centroid C . Suppose that F is a generalized derivation of R and L is a noncentral Lie ideal of R such that F ( u ) [ F ( u ) , u ] n = 0 for all u L , where n 1 is a fixed integer. Then one of the following holds: ...

Generalized D-Symmetric Operators I

Bouali, S., Ech-chad, M. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30.Let H be an infinite-dimensional complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of operators on H into itself. Let δAB: L(H) → L(H) denote the generalized derivation δAB(X) = AX − XB. This note will initiate a study on the class of pairs (A,B) such that [‾(R(δAB))] = [‾(R(δB*A*))]; i.e. [‾(R(δAB))] is self-adjoint.

Generalized eigenfunction expansions and spectral decompositions

Mihai Putinar (1997)

Banach Center Publications

The paper relates several generalized eigenfunction expansions to classical spectral decomposition properties. From this perspective one explains some recent results concerning the classes of decomposable and generalized scalar operators. In particular a universal dilation theory and two different functional models for related classes of operators are presented.

Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces

R. W. Hansell, L. Oncina (2005)

Czechoslovak Mathematical Journal

In this paper we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated.

Generalized Fock spaces, interpolation, multipliers, circle geometry.

Jaak Peetre, Sundaram Thangavelu, Nils-Olof Wallin (1996)

Revista Matemática Iberoamericana

By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e-Q(z), where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle C in C. We consider the problem of interpolation between two Fock spaces. If C0 and C1 are the corresponding circles, one is led to consider the pencil of circles generated by C0 and C1....

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