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Summer 2019 Characterization of $K$-frame vectors and $K$-frame generator multipliers
Farkhondeh Takhteh
Adv. Oper. Theory 4(3): 587-603 (Summer 2019). DOI: 10.15352/aot.1808-1408

Abstract

‎‎Let $\mathcal{U}$ be a unitary system and let $\mathcal{B(U)}$ be the Bessel vector space for $\mathcal{U}$‎. ‎In this article‎, ‎we give a characterization of Bessel vector spaces and local commutant spaces at different complete frame vectors‎. ‎The relation between local commutant spaces at different complete frame vectors is investigated‎. ‎Moreover‎, ‎by introducing multiplication and adjoint on the Bessel vector space for a unital semigroup of unitary operators‎, ‎we give a $C^*$-algebra structure to $\mathcal{B(U)}$‎. ‎Then‎, ‎we construct some subsets of $K$-frame vectors that have a Banach space or Banach algebra structure‎. ‎Also‎, ‎as a consequence‎, ‎the set of complete frame vectors for different unitary systems contains Banach spaces or Banach algebras‎. ‎In the end‎, ‎we give several characterizations of $K$-frame generator multipliers and Parseval $K$-frame generator multipliers‎.

Citation

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Farkhondeh Takhteh. "Characterization of $K$-frame vectors and $K$-frame generator multipliers." Adv. Oper. Theory 4 (3) 587 - 603, Summer 2019. https://doi.org/10.15352/aot.1808-1408

Information

Received: 15 August 2018; Accepted: 18 December 2018; Published: Summer 2019
First available in Project Euclid: 2 March 2019

zbMATH: 07056787
MathSciNet: MR3919033
Digital Object Identifier: 10.15352/aot.1808-1408

Subjects:
Primary: 42C15
Secondary: 41A58 , 42A38

Keywords: $K$-frame vector‎ , Bessel generator multiplier , Bessel vector‎ , ‎‎complete frame vector , ‎‎unitary system

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 3 • Summer 2019
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