Positivity, ( ISI ), Volume (27), No (1), Year (2022-12)

Title : ( Extensions of the Hilbert-multi-norm in Hilbert $$C^*$$-modules )

Authors: sajjad abedi , Mohammad Sal Moslehian ,

Access to full-text not allowed by authors

Citation: BibTeX | EndNote


Dales and Polyakov introduced a multi-norm (∥⋅∥(2,2)n:n∈N) based on a Banach space X and showed that it is equal with the Hilbert-multi-norm (∥⋅∥Hn:n∈N) based on an infinite-dimensional Hilbert space H. We enrich the theory and present three extensions of the Hilbert-multi-norm for a Hilbert C∗-module X. We denote these multi-norms by (∥⋅∥Xn:n∈N), (∥⋅∥∗n:n∈N), and (∥⋅∥P(A)n:n∈N). We show that ∥x∥P(A)n≥∥x∥Xn≤∥x∥∗n for each x∈Xn. In the case when X is a Hilbert K(H)-module, for each x∈Xn, we observe that ∥⋅∥P(A)n=∥⋅∥Xn. Furthermore, if H is separable and X is infinite-dimensional, we prove that ∥x∥Xn=∥x∥∗n. Among other things, we show that small and orthogonal decompositions with respect to these multi-norms are equivalent. Several examples are given to support the new findings.


, Hilbert C∗ , module Hilbert C*, multi, norm Decomposition Orthonormal basis
برای دانلود از شناسه و رمز عبور پرتال پویا استفاده کنید.

author = {Abedi, Sajjad and Sal Moslehian, Mohammad},
title = {Extensions of the Hilbert-multi-norm in Hilbert $$C^*$$-modules},
journal = {Positivity},
year = {2022},
volume = {27},
number = {1},
month = {December},
issn = {1385-1292},
keywords = {Hilbert C∗ -module Hilbert C*-multi-norm Decomposition Orthonormal basis},


%0 Journal Article
%T Extensions of the Hilbert-multi-norm in Hilbert $$C^*$$-modules
%A Abedi, Sajjad
%A Sal Moslehian, Mohammad
%J Positivity
%@ 1385-1292
%D 2022