Atomic systems in $n$-Hilbert spaces and their tensor products

Subject Areas : Functional analysis

P. Ghosh ¹ , T. Samanta ²

1 - Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata, 700019, West Bengal, India
2 - Department of Mathematics, Uluberia College, Uluberia, Howrah, 711315, West Bengal, India

Received: 2021-07-20 Accepted : 2021-11-09 Published : 2021-11-30

Keywords: Atomic system, K-frame, tensor product of Hilbert spaces, linear n-normed space, $n$-Hilbert space,

Abstract :

Concept of a family of local atoms in $n$-Hilbert space is being studied. $K$-frame in tensor product of $n$-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of $n$-Hilbert spaces is presented and established a relationship between atomic systems in $n$-Hilbert spaces and their tensor products.

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