Multipliers of sequence spaces

Cheng, Raymond; Mashreghi, Javad; Ross, William T.

doi:10.1515/conop-2017-0007

Cited by 12 publications

(5 citation statements)

References 17 publications

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“…which turns out to be a well-studied space Banach space of analytic functions on D (see [10] for a survey), the Birkhoff-James orthogonality becomes…”

Section: Inner Vectors In Banach Spacesmentioning

confidence: 99%

Inner Functions in Reproducing Kernel Spaces

Cheng

Mashreghi

Ross

2019

Trends in Mathematics

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In Beurlings approach to inner functions for the shift operator S on the Hardy space H 2 , a function f is inner when f ⊥ S n f for all n 1. Inspired by this approach, this paper develops a notion of an inner vector x for any operator T on a Hilbert space, via the analogous condition x ⊥ T n x for all n 1. We study these inner vectors in a variety of settings. Using Birkhoff-James orthogonality, we extend this notion of inner vector for an operator on a Banach space. We then apply this development of inner function to recast a theorem of Shapiro and Shields to discuss the zero sets for functions in Hilbert spaces, as well as obtain a corresponding result for zero sets for a wide class of Banach spaces.

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“…which turns out to be a well-studied space Banach space of analytic functions on D (see [10] for a survey), the Birkhoff-James orthogonality becomes…”

Section: Inner Vectors In Banach Spacesmentioning

confidence: 99%

Inner Functions in Reproducing Kernel Spaces

Cheng

Mashreghi

Ross

2019

Trends in Mathematics

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“…We point the reader to [9,12] for further background and properties of these spaces. Definition 6.1.…”

Section: Weak Separationmentioning

confidence: 99%

On Interpolation by Functions in $\ell^p_A$

Cheng¹,

Felder²

2022

Preprint

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This work explores several aspects of interpolating sequences for p A , the space of analytic functions on the unit disk with p-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We investigate various analogues of Gramian matrices, for which we show boundedness conditions are necessary and sufficient for interpolation, including a characterization of universal interpolating sequences in terms of Riesz systems. We also discuss weak separation, giving a characterization of such sequences using a generalization of the pseudohyperbolic metric. Lastly, we consider Carleson measures and embeddings.

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“…However, there does not yet exist a complete characterization of M p in terms of the coefficients, or of the boundary function. Our sources on the subject include [19,23,25,26,27,28,29,30,33,34,35], along with the survey paper [12].…”

Section: The Set Of Multipliers Of ℓ Pmentioning

confidence: 99%

On the geometry of the multiplier space of $\ell_A^p$

Cheng,

Felder

2021

Preprint

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Multipliers of sequence spaces

Abstract: This paper is selective survey on the space`p A and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality.

Cited by 12 publications

References 17 publications

Inner Functions in Reproducing Kernel Spaces

Inner Functions in Reproducing Kernel Spaces

On Interpolation by Functions in $\ell^p_A$

On the geometry of the multiplier space of $\ell_A^p$

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