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RISS 인기검색어
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- 저자 : Morteza Mirzaee Azandaryani (검색결과 2 건)
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BESSEL MULTIPLIERS AND APPROXIMATE DUALS IN HILBERT C*-MODULES
Morteza Mirzaee Azandaryani 대한수학회 2017 대한수학회지 Vol.54 No.4
Two standard Bessel sequences in a Hilbert $C^\ast$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^\ast$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce $(a,m)$-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol $m$ by an element $a$ in the center of the $C^\ast$-algebra. We show that approximate duals are special cases of $(a,m)$-approximate duals and we generalize some of the important results obtained for approximate duals to $(a,m)$-approximate duals. Especially we study perturbations of $(a,m)$-approximate duals and $(a,m)$-approximate duals of modular Riesz bases.
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BESSEL MULTIPLIERS AND APPROXIMATE DUALS IN HILBERT C<sup>∗</sup> -MODULES
Azandaryani, Morteza Mirzaee Korean Mathematical Society 2017 대한수학회지 Vol.54 No.4
Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.
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