Banach-valued Bloch-type functions on the unit ball of a Hilbert space and weak spaces of Bloch-type

Authors : Thai QUANG

Pages : 6-21

Doi:10.33205/cma.1243686

View : 11 | Download : 6

Publication Date : 2023-03-15

Article Type : Research Paper

Abstract :In this article, we study the space $\\mathcal B_\\muinsert ignore into journalissuearticles values(B_X,Y);$ of $Y$-valued Bloch-type functions on the unit ball $B_X$ of an infinite dimensional Hilbert space $X$ with $\\mu$ is a normal weight on $B_X$ and $Y$ is a Banach space. We also investigate the characterizations of the space $\\mathcal{WB}_\\muinsert ignore into journalissuearticles values(B_X);$ of $Y$-valued, locally bounded, weakly holomorphic functions associated with the Bloch-type space $\\mathcal B_\\muinsert ignore into journalissuearticles values(B_X);$ of scalar-valued functions in the sense that $f\\in \\mathcal{WB}_\\muinsert ignore into journalissuearticles values(B_X);$ if $w\\circ f \\in \\mathcal B_\\muinsert ignore into journalissuearticles values(B_X);$ for every $w \\in \\mathcal W,$ a separating subspace of the dual $Y\`$ of $Y.$
Keywords : Operators on Hilbert spaces, Bloch spaces, Weak holomorphic