Open AccessSome numerical radius inequalities for products of Hilbert space operators
Author(s) -
Mohsen Hosseini Shah,
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).