Continuous frames in n-Hilbert spaces and their tensor products

Prasenjit Ghosh, Tapas Kumar Samanta

Abstract


We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept of continuous frame for the tensor products of n-Hilbert spaces. Further, we study dual continuous frame and continuous Bessel multiplier in n-Hilbert spaces and their tensor products.


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References


O. Christensen, An introduction to frames and Riesz bases, Birkhauser (2008), DOI: 10.1007/978-0-8176-8224-8.

C. Diminnie, S. Gahler and A. White, 2-inner product spaces, Demonstratio Math. 6 (1973), 525-536.

I. Daubechies, A. Grossmann, Y. Mayer, Painless nonorthogonal expansions, Journal of Mathematical Physics 27 (5) (1986) 1271-1283, DOI: 10.1063/1.527388.

R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, (1952), 341-366, DOI:10.1090/S0002-9947-1952-0047179-6.

G. B. Folland, A Course in abstract harmonic analysis, CRC Press BOCA Raton, Florida.

M. H. Faroughi and E. Osgooei, c-frames and c-Bessel mappings, Bulletin of the Iranian Mathematical Society, Vol. 38, No. 1 (2012), 203-222.

H. Gunawan and Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001), 631-639, DOI:10.1155/S0161171201010675.

P. Ghosh and T. K. Samanta, Construction of frame relative to n-Hilbert space, Journal of Linear and Topological Analysis, Vol. 10, No. 02, (2021), 117-130.

P. Ghosh and T. K. Samanta, Introduction of frame in tensor product of n-Hilbert spaces, Sahand Communications in Mathematical Analysis, DOI: 10.22130/SCMA.2021.524252.909.

P. Ghosh and T. K. Samanta, Atomic systems in n-Hilbert spaces and their tensor products, Journal of Linear and Topological Analysis, Vol. 10, No. 04, (2021), 241-256.

A. Misiak, n-inner product spaces, Math. Nachr., 140(1989), 299-319, DOI: 10.1002/mana.19891400121.

A. Rahimi, A. Najati and Y. N. Dehghan, Continuous frames in Hilbert spaces, Methods of Functional Analysis and Topology, Vol. 12 (2006), no. 2, 170-182.

S. Rabinson, Hilbert space and tensor products, Lecture notes September 8, 1997.

G. Upender Reddy, N. Gopal Reddy and B. Krishna Reddy, Frame operator and Hilbert-Schmidt Operator in Tensor Product of Hilbert Spaces, Journal of Dynamical Systems and Geometric Theories, 7:1, (2009), 61-70, DOI:10.1080/1726037X.2009.10698563.




DOI: https://doi.org/10.52846/ami.v50i1.1637