(E,F)-Schur multipliers and applications

Fedor Sukochev; Anna Tomskova

Displaying similar documents to “(E,F)-Schur multipliers and applications”

The Bogomolov multiplier of groups of order $p^{7}$ and exponent $p$

Zeinab Araghi Rostami, Mohsen Parvizi, Peyman Niroomand (2024)

Czechoslovak Mathematical Journal

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We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order $p^{7}$ $(p > 2)$ and exponent $p$ . We present a comprehensive classification of these groups, identifying those with nontrivial Bogomolov multipliers and distinguishing them from groups with trivial multipliers. Our analysis not only clarifies the conditions under which the Bogomolov multiplier is nontrivial but also refines existing computational methods, enhancing the process of...

Pointwise multipliers on martingale Campanato spaces

Eiichi Nakai, Gaku Sadasue (2014)

Studia Mathematica

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We introduce generalized Campanato spaces $_{p, ϕ}$ on a probability space (Ω,ℱ,P), where p ∈ [1,∞) and ϕ: (0,1] → (0,∞). If p = 1 and ϕ ≡ 1, then $_{p, ϕ} = B M O$ . We give a characterization of the set of all pointwise multipliers on $_{p, ϕ}$ .

Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, Parasar Mohanty (2015)

Studia Mathematica

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In this paper, we introduce and study the notion of completely bounded $Λ_{p}$ sets ( $Λ_{p}^{c b}$ for short) for compact, non-abelian groups G. We characterize $Λ_{p}^{c b}$ sets in terms of completely bounded $L^{p} (G)$ multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are $Λ_{p}$ sets for all p < ∞, but are not $Λ_{p}^{c b}$ for any p ≥ 4. This is done by showing that the space of completely bounded $L^{p} (G)$ ...

An $M_{q} ()$ -functional calculus for power-bounded operators on certain UMD spaces

Earl Berkson, T. A. Gillespie (2005)

Studia Mathematica

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For 1 ≤ q < ∞, let $_{q} ()$ denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes $_{q} ()$ as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction...

Operator Connes-amenability of completely bounded multiplier Banach algebras

Bahman Hayati, Abasalt Bodaghi, Massoud Amini (2019)

Archivum Mathematicum

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For a completely contractive Banach algebra $B$ , we find conditions under which the completely bounded multiplier algebra $ℳ_{c b} (B)$ is a dual Banach algebra and the operator amenability of $B$ is equivalent to the operator Connes-amenability of $ℳ_{c b} (B)$ . We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.

Some isomorphic properties in projective tensor products

Ioana Ghenciu (2022)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient conditions implying that the projective tensor product of two Banach spaces $X$ and $Y$ has the $p$ -sequentially Right and the $p$ - $L$ -limited properties, $1 \leq p < \infty$ .

The space of multipliers and convolutors of Orlicz spaces on a locally compact group

Hasan P. Aghababa, Ibrahim Akbarbaglu, Saeid Maghsoudi (2013)

Studia Mathematica

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Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let $L^{φ} (G)$ and $L^{ψ} (G)$ be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach $L^{φ} (G)$ -submodule X of $L^{ψ} (G)$ , the multiplier space $H o m_{L^{φ} (G)} (L^{φ} (G), X *)$ is a dual Banach space with predual $L^{φ} (G) ∙ X : = \bar{s p a n} u x : u \in L^{φ} (G), x \in X$ , where the closure is taken in the dual space of $H o m_{L^{φ} (G)} (L^{φ} (G), X *)$ . We also prove that if $φ$ is a Δ₂-regular N-function, then $C v_{φ} (G)$ , the space of convolutors of $M^{φ} (G)$ , is identified with the dual of a Banach algebra of functions on G...

The space of multipliers into $l_{1}$

P. Wojtaszczyk (1979)

Annales Polonici Mathematici

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The reciprocal Dunford–Pettis property of order $p$ in projective tensor products

Ioana Ghenciu (2019)

Commentationes Mathematicae Universitatis Carolinae

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We investigate whether the projective tensor product of two Banach spaces $X$ and $Y$ has the reciprocal Dunford–Pettis property of order $p$ , $1 \leq p < \infty$ , when $X$ and $Y$ have the respective property.

The Herz-Schur multiplier norm of sets satisfying the Leinert condition

Éric Ricard, Ana-Maria Stan (2011)

Colloquium Mathematicae

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It is well known that in a free group , one has $| | χ_{E} {| |}_{M_{c b} A ()} \leq 2$ , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for $| | χ_{E} {| |}_{M_{c b} A ()}$ .

Oscillating multipliers on the Heisenberg group

E. K. Narayanan, S. Thangavelu (2001)

Colloquium Mathematicae

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Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{- 1 / 2} s i n \sqrt ℒ$ is bounded on $L^{p} (H ⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

Multipliers of the space $A^{p}$

I. Jovanović (1986)

Matematički Vesnik

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On the H-property and rotundity of Cesàro direct sums of Banach spaces

Saard Youyen, Suthep Suantai (2008)

Banach Center Publications

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In this paper, we define the direct sum ${(⨁_{i = 1}^{n} X_{i})}_{c e s_{p}}$ of Banach spaces X₁,X₂,..., and Xₙ and consider it equipped with the Cesàro p-norm when 1 ≤ p < ∞. We show that ${(⨁_{i = 1}^{n} X_{i})}_{c e s_{p}}$ has the H-property if and only if each $X_{i}$ has the H-property, and ${(⨁_{i = 1}^{n} X_{i})}_{c e s_{p}}$ has the Schur property if and only if each $X_{i}$ has the Schur property. Moreover, we also show that ${(⨁_{i = 1}^{n} X_{i})}_{c e s_{p}}$ is rotund if and only if each $X_{i}$ is rotund.

The classical subspaces of the projective tensor products of $ℓ_{p}$ and C(α) spaces, α < ω₁

Elói Medina Galego, Christian Samuel (2013)

Studia Mathematica

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We completely determine the $ℓ_{q}$ and C(K) spaces which are isomorphic to a subspace of $ℓ_{p} \otimes ̂_{π} C (α)$ , the projective tensor product of the classical $ℓ_{p}$ space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from $ℓ_{p}$ to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...

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 $p$ , $1 \leq p < \infty$ .

Property $(𝐰𝐋)$ and the reciprocal Dunford-Pettis property in projective tensor products

Ioana Ghenciu (2015)

Commentationes Mathematicae Universitatis Carolinae

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A Banach space $X$ has the reciprocal Dunford-Pettis property ( $R D P P$ ) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $R D P P$ (resp. property $(w L)$ ) if every $L$ -subset of $X^{*}$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes_{π} Y$ has property $(w L)$ when $X$ has the $R D P P$ , $Y$ has property $(w L)$ , and $L (X, Y^{*}) = K (X, Y^{*})$ .

A multiplier theorem for Fourier series in several variables

Nakhle Asmar, Florence Newberger, Saleem Watson (2006)

Colloquium Mathematicae

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We define a new type of multiplier operators on $L^{p} (^{N})$ , where $^{N}$ is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on $L^{p} (^{N})$ , to which the theorem applies as a particular example.

Matrix subspaces of L₁

Gideon Schechtman (2013)

Studia Mathematica

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If $E = e_{i}$ and $F = f_{i}$ are two 1-unconditional basic sequences in L₁ with E r-concave and F p-convex, for some 1 ≤ r < p ≤ 2, then the space of matrices $a_{i, j}$ with norm $| | a_{i, j} {| |}_{E (F)} = | | \sum_{k} | | \sum_{l} a_{k, l} f_{l} | | e_{k} | |$ embeds into L₁. This generalizes a recent result of Prochno and Schütt.

$ℓ_{\infty}$ -sums and the Banach space $ℓ_{\infty} / c ₀$

Christina Brech, Piotr Koszmider (2014)

Fundamenta Mathematicae

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This paper is concerned with the isomorphic structure of the Banach space $ℓ_{\infty} / c ₀$ and how it depends on combinatorial tools whose existence is consistent with but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that $ℓ_{\infty} / c ₀$ does not have an orthogonal $ℓ_{\infty}$ -decomposition, that is, it is not of the form $ℓ_{\infty} (X)$ for any Banach space X. The main local result is that it is consistent that $ℓ_{\infty} (c ₀ ())$ does not embed isomorphically into $ℓ_{\infty} / c ₀$ , where is the cardinality of the continuum,...

Recurrence and mixing recurrence of multiplication operators

Mohamed Amouch, Hamza Lakrimi (2024)

Mathematica Bohemica

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Let $X$ be a Banach space, $ℬ (X)$ the algebra of bounded linear operators on $X$ and $(J, ∥ \cdot ∥_{J})$ an admissible Banach ideal of $ℬ (X)$ . For $T \in ℬ (X)$ , let $L_{J, T}$ and $R_{J, T} \in ℬ (J)$ 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 $T \in ℬ (X)$ , 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...