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Displaying similar documents to “Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators”

On a Kleinecke-Shirokov theorem

Vasile Lauric (2021)

Czechoslovak Mathematical Journal

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We prove that for normal operators N 1 , N 2 ( ) , the generalized commutator [ N 1 , N 2 ; X ] approaches zero when [ N 1 , N 2 ; [ N 1 , N 2 ; X ] ] tends to zero in the norm of the Schatten-von Neumann class 𝒞 p with p > 1 and X varies in a bounded set of such a class.

On the range of some elementary operators

Hamza El Mouadine, Abdelkhalek Faouzi, Youssef Bouhafsi (2024)

Commentationes Mathematicae Universitatis Carolinae

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Let L ( H ) denote the algebra of all bounded linear operators on a complex infinite dimensional Hilbert space H . For A , B L ( H ) , the generalized derivation δ A , B and the multiplication operator M A , B are defined on L ( H ) by δ A , B ( X ) = A X - X B and M A , B ( X ) = A X B . In this paper, we give a characterization of bounded operators A and B such that the range of M A , B is closed. We present some sufficient conditions for δ A , B to have closed range. Some related results are also given.

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...

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...

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...

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.

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).

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.

Best constants for the isoperimetric inequality in quantitative form

Marco Cicalese, Gian Paolo Leonardi (2013)

Journal of the European Mathematical Society

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We prove some results in the context of isoperimetric inequalities with quantitative terms. In the 2 -dimensional case, our main contribution is a method for determining the optimal coefficients c 1 , ... , c m in the inequality δ P ( E ) k = 1 m c k α ( E ) k + o ( α ( E ) m ) , valid for each Borel set E with positive and finite area, with δ P ( E ) and α ( E ) being, respectively, the 𝑖𝑠𝑜𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑟𝑖𝑐𝑑𝑒𝑓𝑖𝑐𝑖𝑡 and the 𝐹𝑟𝑎𝑒𝑛𝑘𝑒𝑙𝑎𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦 of E . In n dimensions, besides proving existence and regularity properties of minimizers for a wide class of 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒𝑖𝑠𝑜𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑟𝑖𝑐𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡𝑠 including the lower semicontinuous extension of δ P ( E ) α ( E ) 2 , we...

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.

Repdigits in generalized Pell sequences

Jhon J. Bravo, Jose L. Herrera (2020)

Archivum Mathematicum

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For an integer k 2 , let ( n ) n be the k - generalized Pell sequence which starts with 0 , ... , 0 , 1 ( k terms) and each term afterwards is given by the linear recurrence n = 2 n - 1 + n - 2 + + n - k . In this paper, we find all k -generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence ( P n ( 2 ) ) n . ...

2-summing multiplication operators

Dumitru Popa (2013)

Studia Mathematica

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Let 1 ≤ p < ∞, = ( X ) n be a sequence of Banach spaces and l p ( ) the coresponding vector valued sequence space. Let = ( X ) n , = ( Y ) n be two sequences of Banach spaces, = ( V ) n , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator M : l p ( ) l q ( ) by M ( ( x ) n ) : = ( V ( x ) ) n . We give necessary and sufficient conditions for M to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...

On certain general integral operators of analytic functions

B. A. Frasin (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper, we obtain new sufficient conditions for the operators F α 1 , α 2 , . . . , α n , β ( z ) and G α 1 , α 2 , . . . , α n , β ( z ) to be univalent in the open unit disc 𝒰 , where the functions f 1 , f 2 , . . . , f n belong to the classes S * ( a , b ) and 𝒦 ( a , b ) . The order of convexity for the operators  F α 1 , α 2 , . . . , α n , β ( z ) and G α 1 , α 2 , . . . , α n , β ( z ) is also determined. Furthermore, and for β = 1 , we obtain sufficient conditions for the operators F n ( z ) and G n ( z ) to be in the class 𝒦 ( a , b ) . Several corollaries and consequences of the main results are also considered.