Operator version of the best approximation problem in Hilbert C*-modules (CROSBI ID 207218)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Arambašić, Ljiljana ; Rajić, Rajna
engleski
Operator version of the best approximation problem in Hilbert C*-modules
Let V⊆B(H, K) be a Hilbert C*-module over a C*- algebra A⊆B(H), and X, Y∈V. In this paper we study a problem of finding A∈B(H) such that |X+YB|- |X+YA| is a positive element in A for all B∈A. We show that such an operator exists if and only if the range of Y*X is contained in the range of Y*Y, and in this case it can be chosen to belong to A″. We also consider Hilbert C*-modules in which for every X and Y there is (a unique) A with the above property.
C*-algebra ; Hilbert C*-module ; Best approximation ; Closed range operator
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Podaci o izdanju
413 (1)
2014.
311-320
objavljeno
0022-247X
1096-0813
10.1016/j.jmaa.2013.11.058