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Characterization of inner derivations induced by norm-attainable operators

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Publication Date
2018
Author
Oyake, M. O.
Okelo, Bernad N.
Ongati, Naftali O.
Type
Article
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Abstract/Overview

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.

Subject/Keywords
Banach space; Hilbert space; Inner Derivation; Norms; Tensor Products.
Publisher
International Journal of Modern Science and Technology
ISSN
24560235
Series
3(1):6-9.;
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www.ijmst.co
http://62.24.102.115:8080/xmlui/handle/123456789/1222
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