Title : Achievement of continuity of (phi, psi)-derivations without linearity ( Achievement of continuity of (phi, psi)-derivations without linearity )
Authors: Shirin Hejazian , Ali Reza Janfada , مجید میرزاوزیری , Mohammad Sal Moslehian ,
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Abstract
Suppose that A is a C*-algebra acting on a Hilbert space H, and phi, psi are mappings from A into B(H) which are not assumed to be necessarily linear or continuous. A (phi, psi )-derivation is a linear mapping d : A\\\\mapsto B(H) such that d(ab) =phi(a)d(b) + d(a) psi(b) (a, b in A). We prove that if phi is a multiplicative (not necessarily linear) *-mapping, then every*-(phi,psi\\\')-derivation is automatically continuous. Using this fact, we show that every *-(phi, psi )-derivation d from A into B(H) is continuous if and only if the *-mappings phi and psi are left and right d-continuous, respectively.
Keywords
, Automatic continuity, d-continuous, (phi, psi)-derivation, *-mapping, derivation, C*-algebra.
@article{paperid:1004746,
author = {Hejazian, Shirin and Janfada, Ali Reza and مجید میرزاوزیری and Sal Moslehian, Mohammad},
title = {Achievement of continuity of (phi, psi)-derivations without linearity},
journal = {Bulletin of the Belgian Mathematical Society-Simon Stevin},
year = {2007},
month = {March},
issn = {1370-1444},
keywords = {Automatic continuity; d-continuous; (phi;psi)-derivation; *-mapping;
derivation; C*-algebra.},
}
%0 Journal Article
%T Achievement of continuity of (phi, psi)-derivations without linearity
%A Hejazian, Shirin
%A Janfada, Ali Reza
%A مجید میرزاوزیری
%A Sal Moslehian, Mohammad
%J Bulletin of the Belgian Mathematical Society-Simon Stevin
%@ 1370-1444
%D 2007
