# Characterization of K-frame vectors and K-frame generator multipliers

Document Type: Original Article

Authors

‎Persian Gulf University‎, Iran

Abstract

‎Let $\mathcal{U}$ be a unitary system and let $\mathcal{B(U)}$ be the Bessel vector space for $\mathcal{U}$‎.
‎In this paper‎, ‎we give a characterization of the Bessel vector space and the local commutant space 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 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.

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### History

• Receive Date: 15 August 2018
• Revise Date: 16 December 2018
• Accept Date: 18 December 2018