Some numerical radius inequalities for products of Hilbert space operators | Zendy

Mohsen Hosseini | Zendy; Baharak Moosavi | Zendy

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Some numerical radius inequalities for products of Hilbert space operators

Author(s) -

Mohsen Hosseini,

Baharak Moosavi

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/fil1907089h

Subject(s) - mathematics , hilbert space , radius , linear operators , inequality , space (punctuation) , pure mathematics , spectrum (functional analysis) , mathematical analysis , quantum mechanics , physics , linguistics , philosophy , computer security , computer science , bounded function

We prove several numerical radius inequalities for products of two Hilbert space operators. Some of our inequalities improve well-known ones. More precisely, we prove that, if A,B ? B(H) such that A is self-adjoint with ?1 = min ?i ? ?(A) (the spectrum of A) and ?2 = max ?i ? ?(A). Then ?(AB) ?||A||?(B) + (||A|| - |?1 + ?2|/2)DB where DB = inf ??C ||B - ?I||. In particular, if A > 0 and ?(A) ? [k||A||,||A||], then ?(AB) ? (2 - k)||A|| ?(B).

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