Open AccessThe convex properties and norm bounds for operator matrices involving contractions
Author(s) -
Yuan Li,
Mengqian Cui,
Shasha Hu
Publication year - 2020
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/fil2004271l
Subject(s) - mathematics , norm (philosophy) , hilbert space , regular polygon , combinatorics , convex set , operator (biology) , convex function , matrix norm , subderivative , operator norm , pure mathematics , convex optimization , eigenvalues and eigenvectors , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , political science , transcription factor , law , gene
In this note, the norm bounds and convex properties of special operator matrices ~H(m)n and ~S(m)n are investigated. When Hilbert space K is infinite dimensional, we firstly show that ~H(m)n = ~H(m)n+1 and ~S(m) n = ~S(m)n+1, for m, n = 1,2,.... Then we get that ~H(m) n is a convex and compact set in the ?* topology. Moreover, some norm bounds for ~H(m) n and ~S(m)n are given.