Hilbert Modules over Function Algebras

1986 ◽  
pp. 125-139 ◽  
Author(s):  
Ronald G. Douglas
Keyword(s):  
Hilbert Modules ◽  
Function Algebras

scholarly journals Quantun function algebras as quantum enveloping algebras

1998 ◽  
Vol 26 (6) ◽  
pp. 1795-1818 ◽  
Author(s):  
Fabio Gavarini
Keyword(s):  
Enveloping Algebras ◽  
Function Algebras

On closed ideals in convergence function algebras

1969 ◽  
Vol 182 (3) ◽  
pp. 145-153 ◽  
Author(s):  
E. Binz
Keyword(s):  
Function Algebras ◽  
Convergence Function

Function Algebras on Disks

2002 ◽  
Vol 47 (5) ◽  
pp. 447-451 ◽  
Author(s):  
Quang Dieu Nguyen ◽  
Peter de Paepe
Keyword(s):  
Function Algebras

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

Hilbert \(C^{*}\)-modules in which all relatively strictly closed submodules are complemented

2021 ◽  
Vol 56 (2) ◽  
pp. 343-374
Author(s):  
Boris Guljaš ◽  
Keyword(s):  
Hilbert Space ◽  
Hilbert Modules ◽  
Strict Topology ◽  
Direct Sums ◽  
Essential Ideal ◽  
Closed Submodule ◽  
Closed Submodules ◽  
Hereditary Algebras ◽  
Multiplier Algebras

We give the characterization and description of all full Hilbert modules and associated algebras having the property that each relatively strictly closed submodule is orthogonally complemented. A strict topology is determined by an essential closed two-sided ideal in the associated algebra and a related ideal submodule. It is shown that these are some modules over hereditary algebras containing the essential ideal isomorphic to the algebra of (not necessarily all) compact operators on a Hilbert space. The characterization and description of that broader class of Hilbert modules and their associated algebras is given. As auxiliary results we give properties of strict and relatively strict submodule closures, the characterization of orthogonal closedness and orthogonal complementing property for single submodules, relation of relative strict topology and projections, properties of outer direct sums with respect to the ideals in \(\ell_\infty\) and isomorphisms of Hilbert modules, and we prove some properties of hereditary algebras and associated hereditary modules with respect to the multiplier algebras, multiplier Hilbert modules, corona algebras and corona modules.

Extensions of Hilbert modules

2003 ◽  
pp. 159-187
Author(s):  
Xiaoman Chen ◽  
Kunyu Guo
Keyword(s):  
Hilbert Modules
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