@article {
author = {Javani, Somayeh and Takhteh, Farkhondeh},
title = {Characterization of K-frame vectors and K-frame generator multipliers},
journal = {Advances in Operator Theory},
volume = {4},
number = {3},
pages = {587-603},
year = {2019},
publisher = {Tusi Mathematical Research Group (TMRG)},
issn = {2538-225X},
eissn = {2538-225X},
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 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.},
keywords = {Bessel vector,Complete frame vector,Unitary system,K-frame vector,Bessel generator multiplier},
url = {http://www.aot-math.org/article_80493.html},
eprint = {http://www.aot-math.org/article_80493_0b926f59b299cc7677ae1316e801d4ec.pdf}
}