# Topological Algebras and Applications

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*Anastasios Mallios; Marina Haralampidou*

The Fifth International Conference on Topological Algebras and Applications was held in Athens, Greece, from June 27th to July 1st of 2005. The main topic of the Conference was general theory of topological algebras and its various applications, with emphasis on the “non-normed” case. In addition to the study of the internal structure of non-normed, and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, such as quantum relativity and quantum cosmology. Operator theory of unbounded operators and related non-normed topological algebras are intensively studied here. Other topics presented in this volume are topological homological algebra, topological algebraic geometry, sheaf theory and \(K\)-theory.

#### Readership

Graduate students and research mathematicians interested in topological algebras.

# Table of Contents

## Topological Algebras and Applications

- Contents vii8 free
- Preface xi12 free
- List of Participants xiii14 free
- Conference Lectures xvii18 free
- Topologisation et multiplication dans certaines algèbres 122 free
- On Serre-Swan-Mallios theorem 728
- Topological algebras with idempotently pseudoconvex von Neumann bornology 1536
- Hyers-Ulam-Rassias stability of derivations on Hilbert C* -modules 3152
- On extensions of Stone-Weierstrass theorem 4162
- On Qt-algebras 4970
- Some results on the algebraic approach to quantum dynamics 5778
- Topological algebras and differential structures in C* -algebras 6788
- On C* -spectrality of locally convex *-algebras in C* -algebras 89110
- Pták function, positive elements and the positive cone of a unital LC *-algebra 97118
- Topologizable operators on locally convex spaces 103124
- On locally convex H*-triple systems 109130
- Harmonic functional calculus in m-p-complete A-p-normed algebras 125146
- A concept of finiteness in topological algebras 131152
- Square roots of strongly positive elements in lmc algebras 139160
- Harmonic functions operating on contractions in m-convex algebras 143164
- Some characterizations using cone notions in m-convex algebras 151172
- On the completion of a C* -normed algebra under a locally convex algebra topology 155176
- On Šilov's idempotent theorem 167188
- On generalized Ambrose algebras 181202
- Tensor products in quantum functional analysis: the non-matricial approach 199220
- Unbounded conditional expectations for O* -algebras 225246
- A Radon-Nikodym theorem for completely multi-positive linear maps and its applications 235256
- Commutativity criteria for Gelfand-Mazur algebras 247268
- Topological algebras and quantum cosmology [the Abstract] 253274
- Representation of extensions, of C, endowed with a discrete absolute value 255276
- Another proof of the Shirali-Ford theorem 259280
- On algebra spaces 263284
- On combinatorially regular topological algebras 285306
- Topological algebras with continuous characters 291312
- Spectral decomposition and duality in commutative locally C* -algebras 303324
- Locally A-convex algebras revisited 319340
- On different versions of Vidav-Palmer theorem 331352
- On combinatorially regular Fréchet algebra 339360
- Description of closed maximal one-sided ideals in several classes of real Gelfand-Mazur algebras 345366
- Strictly flat cyclic Fréchet modules and approximate identities 359380
- Homologically trivial Fréchet algebras 367388
- On strictly flat Fréchet modules 389410
- Uniform algebra isomorphisms and peripheral spectra 401422
- Bounded and strongly bounded elements in Banach quasi *-algebras 417438
- On dual coordinate systems 425446
- Operator algebras on locally convex spaces 431452