Displaying similar documents to “2-summing multiplication operators”

The weak Gelfand-Phillips property in spaces of compact operators

Ioana Ghenciu (2017)

Commentationes Mathematicae Universitatis Carolinae

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For Banach spaces X and Y , let K w * ( X * , Y ) denote the space of all w * - w continuous compact operators from X * to Y endowed with the operator norm. A Banach space X has the w G P property if every Grothendieck subset of X is relatively weakly compact. In this paper we study Banach spaces with property w G P . We investigate whether the spaces K w * ( X * , Y ) and X ϵ Y have the w G P property, when X and Y have the w G P property.

Recurrence and mixing recurrence of multiplication operators

Mohamed Amouch, Hamza Lakrimi (2024)

Mathematica Bohemica

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Let X be a Banach space, ( X ) the algebra of bounded linear operators on X and ( J , · J ) an admissible Banach ideal of ( X ) . For T ( X ) , let L J , T and R J , T ( J ) denote the left and right multiplication defined by L J , T ( A ) = T A and R J , T ( A ) = A T , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between T ( X ) , and their elementary operators L J , T and R J , T . In particular, we give necessary and sufficient conditions for L J , T and R J , T to be sequentially recurrent. Furthermore, we prove that L J , T is recurrent...

The boundedness of two classes of integral operators

Xin Wang, Ming-Sheng Liu (2021)

Czechoslovak Mathematical Journal

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The aim of this paper is to characterize the L p - L q boundedness of two classes of integral operators from L p ( 𝒰 , d V α ) to L q ( 𝒰 , d V β ) in terms of the parameters a , b , c , p , q and α , β , where 𝒰 is the Siegel upper half-space. The results in the presented paper generalize a corresponding result given in C. Liu, Y. Liu, P. Hu, L. Zhou (2019).

A characterization of reflexive spaces of operators

Janko Bračič, Lina Oliveira (2018)

Czechoslovak Mathematical Journal

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We show that for a linear space of operators ( 1 , 2 ) the following assertions are equivalent. (i) is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = ( ψ 1 , ψ 2 ) on a bilattice Bil ( ) of subspaces determined by with P ψ 1 ( P , Q ) and Q ψ 2 ( P , Q ) for any pair ( P , Q ) Bil ( ) , and such that an operator T ( 1 , 2 ) lies in if and only if ψ 2 ( P , Q ) T ψ 1 ( P , Q ) = 0 for all ( P , Q ) Bil ( ) . This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces.

Linear maps preserving A -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

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Let be a complex Hilbert space, A a positive operator with closed range in ( ) and A ( ) the sub-algebra of ( ) of all A -self-adjoint operators. Assume φ : A ( ) onto itself is a linear continuous map. This paper shows that if φ preserves A -unitary operators such that φ ( I ) = P then ψ defined by ψ ( T ) = P φ ( P T ) is a homomorphism or an anti-homomorphism and ψ ( T ) = ψ ( T ) for all T A ( ) , where P = A + A and A + is the Moore-Penrose inverse of A . A similar result is also true if φ preserves A -quasi-unitary operators in both directions such that there...

A note on Dunford-Pettis like properties and complemented spaces of operators

Ioana Ghenciu (2018)

Commentationes Mathematicae Universitatis Carolinae

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Equivalent formulations of the Dunford-Pettis property of order p ( D P P p ), 1 < p < , are studied. Let L ( X , Y ) , W ( X , Y ) , K ( X , Y ) , U ( X , Y ) , and C p ( X , Y ) denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and p -convergent operators from X to Y . Classical results of Kalton are used to study the complementability of the spaces W ( X , Y ) and K ( X , Y ) in the space C p ( X , Y ) , and of C p ( X , Y ) in U ( X , Y ) and L ( X , Y ) .

Limited p -converging operators and relation with some geometric properties of Banach spaces

Mohammad B. Dehghani, Seyed M. Moshtaghioun (2021)

Commentationes Mathematicae Universitatis Carolinae

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By using the concepts of limited p -converging operators between two Banach spaces X and Y , L p -sets and L p -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as * -Dunford–Pettis property of order p and Pelczyński’s property of order p , 1 p < .

Multiplication operators on L ( L p ) and p -strictly singular operators

William Johnson, Gideon Schechtman (2008)

Journal of the European Mathematical Society

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A classification of weakly compact multiplication operators on L ( L p ) , 1<p< , i s g i v e n . T h i s a n s w e r s a q u e s t i o n r a i s e d b y S a k s m a n a n d T y l l i i n 1992 . T h e c l a s s i f i c a t i o n i n v o l v e s t h e c o n c e p t o f p - s t r i c t l y s i n g u l a r o p e r a t o r s , a n d w e a l s o i n v e s t i g a t e t h e s t r u c t u r e o f g e n e r a l p - s t r i c t l y s i n g u l a r o p e r a t o r s o n Lp . T h e m a i n r e s u l t i s t h a t i f a n o p e r a t o r T o n Lp , 1<p<2 , i s p - s t r i c t l y s i n g u l a r a n d T|X i s a n i s o m o r p h i s m f o r s o m e s u b s p a c e X o f Lp , t h e n X e m b e d s i n t o Lr f o r a l l r<2 , b u t X n e e d n o t b e i s o m o r p h i c t o a H i l b e r t s p a c e . It is also shown that if T is convolution by a biased coin on L p of the Cantor group, 1 p < 2 , and T | X is an isomorphism for some reflexive subspace X of L p , then X is isomorphic to a Hilbert space. The case p = 1 answers a question asked by Rosenthal in 1976.

L -limited-like properties on Banach spaces

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the p - L -limited * and the p -(SR * ) properties and characterize these classes of Banach spaces in terms of p - L -limited * and p -Right * subsets. The p - L -limited * property is studied in some spaces of operators.

On the range-kernel orthogonality of elementary operators

Said Bouali, Youssef Bouhafsi (2015)

Mathematica Bohemica

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Let L ( H ) denote the algebra of operators on a complex infinite dimensional Hilbert space H . For A , B L ( H ) , the generalized derivation δ A , B and the elementary operator Δ A , B are defined by δ A , B ( X ) = A X - X B and Δ A , B ( X ) = A X B - X for all X L ( H ) . In this paper, we exhibit pairs ( A , B ) of operators such that the range-kernel orthogonality of δ A , B holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of Δ A , B with respect to the wider class of unitarily invariant...

Coleff-Herrera currents, duality, and noetherian operators

Mats Andersson (2011)

Bulletin de la Société Mathématique de France

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Let be a coherent subsheaf of a locally free sheaf 𝒪 ( E 0 ) and suppose that = 𝒪 ( E 0 ) / has pure codimension. Starting with a residue current R obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current μ with support on the variety associated to such that φ is in if and only if μ φ = 0 . Such a current μ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed....