✦ LIBER ✦

Differential Banach *-Algebras of Compact Operators Associated with Symmetric Operators

✍ Scribed by Edward Kissin; Victor S Shulman

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 455 KB
Volume: 156
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3186

No coin nor oath required. For personal study only.

✦ Synopsis

Extensive development of noncommutative geometry requires elaboration of the theory of differential Banach *-algebras, that is, dense *-subalgebras of C*-algebras whose properties are analogous to the properties of algebras of differentiable functions. We consider a specific class of such algebras, D-algebras, and show that various *-algebras of compact operators associated with symmetric operators S on Hilbert spaces H are D-subalgebras of the C*-algebra of all compact operators C(H). We focus on how the properties of the operators S are reflected in the structure of these operator algebras.

where D 0 and where r(x*x) is the spectral radius of x*x in A. It was shown that these algebras can be equivalently described as dense article no. FU973186

📜 SIMILAR VOLUMES

A Class of Pseudo-Differential Operators

A Class of Pseudo-Differential Operators Associated with Bessel Operators

✍ R.S. Pathak; P.K. Pandey 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 312 KB

Computability of compact operators on co

Computability of compact operators on computable Banach spaces with bases

✍ Vasco Brattka; Ruth Dillhage 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB

## Abstract We develop some parts of the theory of compact operators from the point of view of computable analysis. While computable compact operators on Hilbert spaces are easy to understand, it turns out that these operators on Banach spaces are harder to handle. Classically, the theory of compac

Some Polynomial Systems Associated with

Some Polynomial Systems Associated with a Certain Family of Differential Operators

✍ Kung-Yu Chen; Chuan-Jen Chyan; H.M. Srivastava 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 204 KB

The authors aim at presenting several (presumably new) classes of linear, bilinear, and mixed multilateral generating functions for some general systems of polynomials which are defined by means of a certain family of differential operators. Some of the generating functions considered here are assoc

Lpμ-Boundedness of the Pseudo-differenti

Lpμ-Boundedness of the Pseudo-differential Operator Associated with the Bessel Operator

✍ R.S. Pathak; S.K. Upadhyay 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 101 KB

Symbol calculus and Fredholmness for a B

Symbol calculus and Fredholmness for a Banach algebra of convolution type operators with slowly oscillating and piecewise continuous data

✍ Maria Amélia Bastos; António Bravo; Yuri Karlovich 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 358 KB

## Abstract A symbol calculus for the smallest Banach subalgebra 𝒜~[__SO,PC__]~ of the Banach algebra ℬ︁(__L^n^~p~__(ℝ)) of all bounded linear operators on the Lebesgue spaces __L^n^~p~__(ℝ) (1 < __p__ < ∞, __n__ ≥ 1) which contains all the convolution type operators __W~a,b~__ = __a__ℱ^−1^__b__ℱ w

A parametrix construction for the fundam

A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo-differential operator generating a Markov process

✍ Björn Böttcher 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 138 KB

## Abstract We use the method proposed by H. Kumano‐go in the classical case to construct a parametrix of the equation $ \textstyle {{\partial u} \over {\partial t}}$ + __q__ (__x, D__ )__u__ = 0 where __q__ (__x, D__ ) is a pseudo‐differential operator with symbol in the class introduced by W. Hoh