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Abstract:
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In this paper we present some norm inequalities for certain elementary operators and
inner product type transformers, specially for Schatten norms, if the families of operators
generating those transforms consists of arbitrary operators, and Q norms if at least
one of those families consists of mutually commuting normal operators. Among others,
we present inequalities that are generalizing the inequality
p
IA AX
p
IB B
6
X AXB
;
from [11, Th. 2.3], for normal contractions and arbitrary unitarily invariant norm, to
the case of Schatten norms and arbitrary contractions, as well as Q norms if at least
one of the contractions A or B is normal.
Also, by applying norm inequalities for operator monotone and operator convex
functions, some refined Cauchy - Schwarz operator inequalities, as well as Minkowski
and Landau - Gruss norm inequalities for operators are obtained as well. |