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Start Over Search Limiters Full Text Topic hilbert c∗-modules Publication Year Range Last 10 years Language english
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4. Near continuous g-frames for Hilbert C∗-modules.

Author

Khatib, Y., Hassani, M., and Amyari, M.

Subjects
HILBERT space, LINEAR operators, NONLINEAR operators, MATHEMATICS, MAPS
Abstract

Let U be a Hilbert A-module and L(U) the set of all adjointable A-linear maps on U. Let K = {Λx ∈ L(U, Vx) : x ∈ X } and L = {Γx ∈ L(U, Vx) : x ∈ X } be two continuous g-frames for U, K is said to be similar with L if there exists an invertible operator J ∈ L(U) such that Γx = ΛxJ, for all x ∈ X . In this paper, we define the concepts of closeness and nearness between two continuous g-frames. In particular, we show that K and L are near, if and only if they are similar. [ABSTRACT FROM AUTHOR]

Published
2019

11. Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators

Author

Jens Kaad

Subjects
Pure mathematics, Hilbert C∗C∗-modules, Existential quantification, 01 natural sciences, Square (algebra), Domain (mathematical analysis), Graßmann connections, 0103 physical sciences, FOS: Mathematics, Grassmann connections, Differentiable function, Absorption (logic), 0101 mathematics, Operator Algebras (math.OA), Mathematical Physics, Mathematics, Sequence, Algebra and Number Theory, Mathematics::Operator Algebras, 010102 general mathematics, Mathematics - Operator Algebras, derivations, Hilbert C∗-modules, Construct (python library), Base (topology), Functional Analysis (math.FA), Mathematics - Functional Analysis, Primary: 46L08, 46L87, Secondary: 53C05, 47A05, 46L57, 58B34, Differentiable absorption, Regular unbounded operators, 010307 mathematical physics, Geometry and Topology
Abstract

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C*-module is isomorphic to a direct summand in the standard module of square summable sequences in the base C*-algebra. In this paper, this result will be generalized by incorporating a densely defined derivation on the base C*-algebra. This leads to a differentiable version of the Kasparov absorption theorem. The extra compatibility assumptions needed are minimal: It will only be required that there exists a sequence of generators with mutual inner products in the domain of the derivation. The differentiable absorption theorem is then applied to construct densely defined connections (or correspondences) on Hilbert C*-modules. These connections can in turn be used to define selfadjoint and regular "lifts" of unbounded operators which act on an auxiliary Hilbert C*-module., Comment: 25 pages

Published
2017