Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-16T23:23:47.923Z Has data issue: false hasContentIssue false
  • English
  • Français

Slice Maps and Multipliers of Invariant Subspaces

Published online by Cambridge University Press:  20 November 2018

Takahiko Nakazi
Takahiko Nakazi*
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let be the closed bidisc and T2 be its distinguished boundary. For be a slice map, that is, and Then ker Φαβ is an invariant subspace, and it is not difficult to describe ker Φαβ and In this paper, we study the set of all multipliers for an invariant subspace M such that the common zero set of M contains that of ker Φαβ.

Keywords

47A1532A35Hardy spaceseveral variablesinvariant subspaceslice map
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 219 - 226
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Beurling, A., On two problems concerning linear transformations in Hilbert space, Acta Math. 81(1949), 239–255.Google Scholar
2. Douglas, R. G. and K. Yan, On the rigidity of Hardy submodules, Integral Eq Op. Th. 13(1990), 350–363.Google Scholar
3. Horowitz, C., Zeros of functions in the Bergman spaces, Duke Math. J. 41(1974). 4. T. Nakazi, Multipliers of invariant subspaces in the bidisc, Proc. Edinburgh Math. Soc. 37(1994), 193—199.Google Scholar
5. Range, M., A small boundary for H°° on the polydisc, Proc. Amer. Math. Soc. 32(1972), 253–255.Google Scholar
6. Rudin, W., Function Theory in Polydisks, Benjamin, New York (1969).Google Scholar