Introduction of Frame in Tensor Product of $n$-Hilbert Spaces

Abstract

We study the concept of frame in tensor product of $n$-Hilbert spaces as tensor product of $n$-Hilbert spaces is again an $n$-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of $n$-Hilbert spaces is studied. Finally,\;the dual frame in tensor product of $n$-Hilbert spaces is discussed.

Keywords

• frame
• dual frame
• tensor product of hilbert spaces
• $n$-normed space
• $n$-hilbert space