Projectivity and lifting of Hilbert module maps

• Autorzy: Douglas N. Clark
• Języki publikacji: EN

Abstrakty

EN

In a recent paper, Carlson, Foiaş, Williams and the author proved that isometric Hilbert modules are projective in the category of Hilbert modules similar to contractive ones. In this paper, a simple proof, based on a strengthened lifting theorem, is given. The proof also applies to an equivalent theorem of Foiaş and Williams on similarity to a contraction of a certain 2 × 2 operator matrix.

Słowa kluczowe

EN

Hilbert module; lifting theorem; polynomially bounded

Kategorie tematyczne

• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)
• 47A20: Dilations, extensions, compressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 43-48

Daty

wydano

1997

otrzymano

1995-02-15

Twórcy

autor

Douglas N. Clark

• Department of Mathematics, University of Georgia, Athens, Georgia 30602, U.S.A.

Bibliografia

• [1] J. F. Carlson and D. N. Clark, Cohomology and extensions of Hilbert modules, J. Funct. Anal. 128 (1995), 278-306.
• [2] J. F. Carlson, D. N. Clark, C. Foiaş and J. P. Williams, Projective Hilbert 𝔸(𝔻)-modules, New York J. Math. 1 (1994), 26-38.
• [3] R. G. Douglas and V. I. Paulsen, Hilbert Modules over Function Algebras, Longman Scientific and Technical, New York, 1989.