Displaying similar documents to “Unbounded multipliers and summation of series”

Multipliers of sequence spaces

Raymond Cheng, Javad Mashreghi, William T. Ross (2017)

Concrete Operators

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This paper is selective survey on the space lAp and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality

Schur and operator multipliers

Ivan G. Todorov, Lyudmila Turowska (2010)

Banach Center Publications

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The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative...

Distinctness of spaces of Lorentz-Zygmund multipliers

Kathryn E. Hare, Parasar Mohanty (2005)

Studia Mathematica

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We study the spaces of Lorentz-Zygmund multipliers on compact abelian groups and show that many of these spaces are distinct. This generalizes earlier work on the non-equality of spaces of Lorentz multipliers.

Multipliers on a Hilbert Space of Functions on R

Petkova, Violeta (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 42A45. For a Hilbert space H ⊂ L1loc(R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L2(R) as well as our previous result for multipliers in weighted space L2ω(R). Moreover, we obtain a description of the spectrum of S.

A remark on the multipliers of the Haar basis of L¹[0,1]

H. M. Wark (2015)

Studia Mathematica

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A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.

The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos, Nigel J. Kalton (2001)

Studia Mathematica

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This article is concerned with the question of whether Marcinkiewicz multipliers on ℝ 2 n give rise to bilinear multipliers on ℝⁿ × ℝⁿ. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy...