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Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
International Journal of Modern Science and Technology,
Abstract
In the present paper, results on characterization of inner derivations in Banach algebras are discussed.
Some techniques are employed for derivations due to Mecheri, Hacene, Bounkhel and Anderson. Let H
be an infinite dimensional complex Hilbert space and B(H) the algebra of all bounded linear operators
on H. A generalized derivation δ: B(H) → B(H) is defined by δA,B(X) = AX −XB, for all X ∈ B(H) and
A,B fixed in B(H). An inner derivation is defined by δA(X) = AX −XA, for all X ∈ B(H) and A fixed in
B(H). Norms of inner derivations have been investigated by several mathematicians. However, it is
noted that norms of inner derivations implemented by norm-attainable operators have not been
considered to a great extent. In this study, we investigate properties of inner derivations which are
strictly implemented by norm-attainable and we determine their norms. The derivations in this work are
all implemented by norm-attainable operators. The results show that these derivations admit tensor
norms of operators.
Description
Keywords
Banach space, Hilbert space, Inner Derivation, Norms, Tensor Products.