Gelfand Triple Isomorphisms for Weighted Banach Spaces on Locally Compact Groups

Abstract

As in [1], we use the concept of wavelet transform on a locally compact group G to construct weighted Banach spaces H1w (G), we being a submultiple weight function on G. The main result of this paper provides an extension of a unitary mapping U from H(G1) to H(G2) under suitable conditions to an isomorphism between the Gelfand triple (H1w ;H;H1w )(G1)and (H1w;H;H1w )(G2); where G1; G2 are any two locally compact groups, H a Hilbert space and H1w is the space of all continuous-conjugate linear functional on H1w . This paper paves the way for the study of some other properties of Gelfand triples.