caa a22 4500 469043571 CHVBK 20180323132817.0 cr unu---uuuuu 170328e19920901xx s 000 0 eng 10.1007/BF01200696 doi (NATIONALLICENCE)springer-10.1007/BF01200696 A note on operator norm inequalities [Elektronische Daten] [Richard Fleming, Sivaram Narayan, Sing-Cheong Ong] If P is a positive operator on a Hilbert space H whose range is dense, then a theorem of Foias, Ong, and Rosenthal says that: ‖[ϕ(P)]−1T[ϕ(P)]‖<-12 max {‖T‖, ‖P−1TP‖} for any bounded operator T on H, where φ is a continuous, concave, nonnegative, nondecreasing function on [0, ‖P‖]. This inequality is extended to the class of normal operators with dense range to obtain the inequality ‖[φ(N)]−1T[φ(N)]‖<-12c2 max {tT‖, ‖N−1TN‖} where φ is a complex valued function in a class of functions called vase-like, and c is a constant which is associated with φ by the definition of vase-like. As a corollary, it is shown that the reflexive lattice of operator ranges generated by the range NH of a normal operator N consists of the ranges of all operators of the form φ(N), where φ is vase-like. Similar results are obtained for scalar-type spectral operators on a Hilbert space. Birkhäuser Verlag, 1992 Primary, 47 A 30 nationallicence Secondary, 47 A 50 nationallicence Fleming Richard Department of Mathematics, Central Michigan University, 48859, Mount Pleasant, MI, U.S.A. aut Narayan Sivaram Department of Mathematics, Central Michigan University, 48859, Mount Pleasant, MI, U.S.A. aut Ong Sing-Cheong Department of Mathematics, Central Michigan University, 48859, Mount Pleasant, MI, U.S.A. aut Integral Equations and Operator Theory Birkhäuser-Verlag 15/5(1992-09-01), 722-729 0378-620X 15:5<722 1992 15 20 https://doi.org/10.1007/BF01200696 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01200696 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fleming Richard Department of Mathematics, Central Michigan University, 48859, Mount Pleasant, MI, U.S.A aut NATIONALLICENCE 700 1- Narayan Sivaram Department of Mathematics, Central Michigan University, 48859, Mount Pleasant, MI, U.S.A aut NATIONALLICENCE 700 1- Ong Sing-Cheong Department of Mathematics, Central Michigan University, 48859, Mount Pleasant, MI, U.S.A aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/5(1992-09-01), 722-729 0378-620X 15:5<722 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer