Open Access
Original Articles
Frame Operator and Hilbert-Schmidt Operator in Tensor Product of Hilbert Spaces
G. Upender Reddyupendergujjula@yahoo.co.inDepartment of Mathematics, Aurora’s Technological And Research InstituteUppal, HyderabadView full profile → , N. Gopal ReddyDepartment of Mathematics, Osmania University, Hyderabad and Lalitha P.G. College VenkatapurHyderabadView full profile → , B. Krishna ReddyDepartment of mathematics, University college of engineering, Osmania UniversityHyderabadView full profile →
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- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2009.10698563
- Pages:
- 61–70
Abstract
The tensor product of frames in Hilbert spaces is introduced. It was shown that the tensor product of two frames is a frame for the tensor product of Hilbert spaces. The concept of tensor frame operator on tensor product of Hilbert space is given and results of it are presented. Inequalities between tensor product of frames and the Hilbert-Schmidt operators are established.
Keywords
References
Amir, K. and Khosravi, Behrooz. 2007 . Frame Bases in tensor products of Hilbert Spaces and Hilbert C - modules . Pro. Indian Acad. Sci. (math. Sci), 117 ( 1 ) February : 1 – 12 . Amson, J. C. and Gopal Reddy, N. 1990 . A Hilbert algebra of Hilbert-Schmidt Quadratic operators . Bull. Australian. Math. Soc, 41 : 123 – 134 . Balazs, P.2006 . Hilbert-Schmidt Operators and Frames Classification, Approximation by Multiplies and AlgorithmsPreprint Casazza, P. G.2000 . The art of frame theory . Taiwanese journal of Math, 4 ( 2 ) : 192 – 202 . Christensen, O.2002 . An introduction to frames and Riesz bases, Birkhauser . Rabinson, S.1997 . Hilbert space and tensor products, Lecture notes September 8
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