Holomorphic Functions and polynomial ideals on Banach spaces

Details Holomorphic Functions and polynomial ideals on Banach spaces Holomorphic Functions and polynomial ideals on Banach spaces

2009-10-20

arxiv.org/abs/0910.3963v2

Collect. Math. (2012) 63:71-91

Mathematics

Functional Analysis

19 pages

Scientific paper

10.1007/s13348-010-0025-5

Given $\u$ a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, $H_{b\u}(E)$. We prove that, under very natural conditions verified by many usual classes of polynomials, the spectrum $M_{b\u}(E)$ of this algebra "behaves" like the classical case of $M_{b}(E)$ (the spectrum of $H_b(E)$, the algebra of bounded type holomorphic functions). More precisely, we prove that $M_{b\u}(E)$ can be endowed with a structure of Riemann domain over $E"$ and that the extension of each $f\in H_{b\u}(E)$ to the spectrum is an $\u$-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.

Affiliated with

Also associated with

No associations

Rating

Holomorphic Functions and polynomial ideals on Banach spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Holomorphic Functions and polynomial ideals on Banach spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holomorphic Functions and polynomial ideals on Banach spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-143454