On Šilov Resolution of Hilbert Modules

1988 ◽  
pp. 51-60 ◽  
Author(s):  
R. G. Douglas
Keyword(s):  
Hilbert Modules

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

Rigidity for analytic Hilbert modules

2003 ◽  
pp. 49-73
Author(s):  
Xiaoman Chen ◽  
Kunyu Guo
Keyword(s):  
Hilbert Modules

On reducing submodules of Hilbert modules withSn-invariant kernels

2019 ◽  
Vol 276 (3) ◽  
pp. 751-784
Author(s):  
Shibananda Biswas ◽  
Gargi Ghosh ◽  
Gadadhar Misra ◽  
Subrata Shyam Roy
Keyword(s):  
Hilbert Modules ◽  
Invariant Kernels

Quasi-homogeneous Hilbert Modules

2007 ◽  
Vol 58 (3) ◽  
pp. 301-314 ◽  
Author(s):  
Yongjiang Duan
Keyword(s):  
Hilbert Modules

scholarly journals Comment on “Continuous g-Frame in Hilbert -Modules”

2013 ◽  
Vol 2013 ◽  
pp. 1-2
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Riesz Basis ◽  
Hilbert Modules

The continuous g-frames in Hilbert -modules were introduced and investigated by Kouchi and Nazari (2011). They also studied the continuous g-Riesz basis and a characterization for it was presented by using the synthesis operator. However, we found that there is an error in the proof. The purpose of this paper is to improve their result by introducing the so-called modular continuous g-Riesz basis.

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