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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 $u \in L$ , where $n \geq 1$ is a fixed integer. Then one of the following holds: (1) ...

Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras

Feng Wei, Zhankui Xiao (2009)

Rendiconti del Seminario Matematico della Università di Padova

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 fractional linear transformations: convexity and compactness of the image and the pre-image; applications.

V. Khatskevich (1999)

Studia Mathematica

The convexity and compactness in the weak operator topology of the image and pre-image of a generalized fractional linear transformation is established. As an application the exponential dichotomy of solutions to evolution problems of the parabolic type is proved.

Generalized Gram-Hadamard inequality.

Constantinescu, Florin, Scharf, Günter (1998)

Journal of Inequalities and Applications [electronic only]

Generalized Hardy operators and normalizing measures.

Chen, Tieling, Sinnamon, Gord (2002)

Journal of Inequalities and Applications [electronic only]

Generalized Hausdorff Matrices as Bounded Operators on lP.

David Borwein (1983)

Mathematische Zeitschrift

Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions

Sunanda Naik, Karabi Rajbangshi (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Let f be an analytic function on the unit disk . We define a generalized Hilbert-type operator $_{a, b}$ by $_{a, b} (f) (z) = Γ (a + 1) / Γ (b + 1) \int_{0}^{1} (f (t) {(1 - t)}^{b}) / ({(1 - t z)}^{a + 1}) d t$ , where a and b are non-negative real numbers. In particular, for a = b = β, $_{a, b}$ becomes the generalized Hilbert operator $_{β}$ , and β = 0 gives the classical Hilbert operator . In this article, we find conditions on a and b such that $_{a, b}$ is bounded on Dirichlet-type spaces $S^{p}$ , 0 < p < 2, and on Bergman spaces $A^{p}$ , 2 < p < ∞. Also we find an upper bound for the norm of the operator $_{a, b}$ . These generalize...

Generalized Hyers-Ulam stability of generalized $(N, K)$ -derivations.

Gordji, M.Eshaghi, Rassias, J.M., Ghobadipour, N. (2009)

Abstract and Applied Analysis

Generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras

Asia Majieed, Jiren Zhou (2010)

Czechoslovak Mathematical Journal

In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk. J. Math. 30 (2006), 403–411). We show that if $𝒰$ is a triangular algebra, then every generalized Jordan derivation of above type from $𝒰$ into itself is a generalized derivation.

Generalized Lions-Peetre methods of constants and means and operator ideals.

Antonio Manzano, Mieczyslaw Mastylo (2007)

Collectanea Mathematica

We establish results on interpolation of Rosenthal operators, Banach-Saks operators, Asplund operators and weakly compact operators by means of generalized Lions-Peetre methods of constants and means. Applications are presented for the K-method space generated by the Calderón-Lozanovskii space parameters.

Generalized quadratic operators and perturbations

Khalid Souilah (2022)

Mathematica Bohemica

We provide a complete description of the perturbation class and the commuting perturbation class of all generalized quadratic bounded operators with respect to a given idempotent bounded operator in the context of complex Banach spaces. Furthermore, we give simple characterizations of the generalized quadraticity of linear combinations of two generalized quadratic bounded operators with respect to a given idempotent bounded operator.

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