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Displaying 3821 – 3840 of 11160

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Generalized gradients for locally Lipschitz integral functionals on non- L p -type spaces of measurable functions

Hôǹg Thái Nguyêñ, Dariusz Pączka (2008)

Banach Center Publications

Let (Ω,μ) be a measure space, E be an arbitrary separable Banach space, E * ω * be the dual equipped with the weak* topology, and g:Ω × E → ℝ be a Carathéodory function which is Lipschitz continuous on each ball of E for almost all s ∈ Ω. Put G ( x ) : = Ω g ( s , x ( s ) ) d μ ( s ) . Consider the integral functional G defined on some non- L p -type Banach space X of measurable functions x: Ω → E. We present several general theorems on sufficient conditions under which any element γ ∈ X* of Clarke’s generalized gradient (multivalued C-subgradient)...

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Mohammad Ashraf, Nazia Parveen, Bilal Ahmad Wani (2017)

Communications in Mathematics

Let 𝔄 = 𝒜 be the triangular algebra consisting of unital algebras 𝒜 and over a commutative ring R with identity 1 and be a unital ( 𝒜 , ) -bimodule. An additive subgroup 𝔏 of 𝔄 is said to be a Lie ideal of 𝔄 if [ 𝔏 , 𝔄 ] 𝔏 . A non-central square closed Lie ideal 𝔏 of 𝔄 is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on 𝔄 , every generalized Jordan triple higher derivation of 𝔏 into 𝔄 is a generalized higher derivation of 𝔏 into 𝔄 .

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 ) 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 induced norms

S. Hejazian, M. Mirzavaziri, Mohammad Sal Moslehian (2007)

Czechoslovak Mathematical Journal

Let · be a norm on the algebra n of all n × n matrices over . An interesting problem in matrix theory is that “Are there two norms · 1 and · 2 on n such that A = max { A x 2 x 1 = 1 } for all A n ?” We will investigate this problem and its various aspects and will discuss some conditions under which · 1 = · 2 .

Generalized inverses in C*-algebras II

Robin Harte, Mostafa Mbekhta (1993)

Studia Mathematica

Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.

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 limits and a mean ergodic theorem

Yuan-Chuan Li, Sen-Yen Shaw (1996)

Studia Mathematica

For a given linear operator L on with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on and X = , the definition of L-limit reduces to Lorentz’s definition of σ-limit, which is described by means of Banach limits on . We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version of the abstract...

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.

Currently displaying 3821 – 3840 of 11160