The Cayley transform of Banach algebras.
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of -algebras
The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in -algebras. Since -algebras are natural generalizations of -algebras, -algebras, -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.
The hypo-Euclidean norm of an -tuple of vectors in inner product spaces and applications.
The Schur multiplication in tensor algebras
The Szegö and Beurling theorems and operator factorizations
The trace of finite and nuclear elements in Banach algebras
The von Neumann algebra associated with an infinite number of t-free noncommutative gaussian random variables
We show that the von Neumann algebras generated by an infinite number of t-deformed free gaussian operators are factors of type .