Operator inequalities related to p-angular distances | Zendy

Taba Afkhami | Zendy; Hossein Dehghan | Zendy

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Operator inequalities related to p-angular distances

Author(s) -

Taba Afkhami,

Hossein Dehghan

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1907107a

Subject(s) - mathematics , lemma (botany) , operator (biology) , inner product space , product (mathematics) , skew , combinatorics , pure mathematics , mathematical analysis , geometry , physics , repressor , ecology , biochemistry , chemistry , poaceae , astronomy , gene , transcription factor , biology

For any nonzero elements x,y in a normed space X, the angular and skew-angular distance is respectively defined by ?[x,y] = ||x/||x|| - y/||y|||| and ?[x,y] = ||x/||y|| - y/||x||||. Also inequality ? ? ? characterizes inner product spaces. Operator version of ? p has been studied by Pecaric, Rajic, and Saito, Tominaga, and Zou et al. In this paper, we study the operator version of p-angular distance ?p by using Douglas? lemma. We also prove that the operator version of inequality ? p ? ?p holds for normal and double commute operators. Some examples are presented to show essentiality of these conditions.

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