ACTA issues

Pusz--Woronowicz's functional calculus revisited

Kanae Hatano, Yoshimichi Ueda

Acta Sci. Math. (Szeged) 87:3-4(2021), 485-503

Abstract. This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their functional calculus, we show that any operator connection type operations (including any operator perspectives) are captured by their functional calculus.

DOI: 10.14232/actasm-021-263-6

AMS Subject Classification (1991): 47A60; 47A64

Keyword(s): functional calculus, operator connection, operator perspective, convexity

received 3.1.2021, revised 28.8.2021, accepted 31.8.2021. (Registered under 13/2021.)