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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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참고문헌 (39)
참고문헌 신청
L. Arambasic / 2007 / On frames for countably generated Hilbert C∗-modules / Proc. Amer. Math. Soc 135(2):469~478
P. Balazs / 2007 / Basic definition and properties of Bessel multipliers / J. Math. Anal. Appl 325(1):571~585
P. Balazs / 2008 / Hilbert Schmidt operators and frames classification, approximation by multipli-ers and algorithms / Int. J. Wavelets Multiresolut. Inf. Process 6(2):315~330
P. Balazs / 2010 / Weighted and controlled frames, mutual re-lationship and first numerical properties / Int. J. Wavelets Multiresolut. Inf. Process 8(1):109~132
P. Balazs / 2012 / Multipliers for continuos frames in Hilbert spaces / J. Phys. A: Math. Theor 45:20
P. Balazs / 2007 / Basic definition and properties of Bessel multipliers / J. Math. Anal. Appl 325(1):571~585
P. Balazs / 2008 / Hilbert Schmidt operators and frames classification, approximation by multipli-ers and algorithms / Int. J. Wavelets Multiresolut. Inf. Process 6(2):315~330
P. Balazs / 2010 / Weighted and controlled frames, mutual re-lationship and first numerical properties / Int. J. Wavelets Multiresolut. Inf. Process 8(1):109~132
P. Balazs / 2012 / Multipliers for continuos frames in Hilbert spaces / J. Phys. A: Math. Theor 45:20
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