Aspects of positivity in functional analysis: proceedings of the conference held on the occasion of H.H. Schaefer’s 60th birthday, Tubingen, 24-28 June 1985

R. Nagel, U. Schloterbeck and M.P.H. Wolff (Eds.)0444879595, 9780444879592, 9780080872339

The contributions collected in this volume exhibit the increasingly wide spectrum of applications of abstract order theory in analysis and show the possibilities of order-theoretical argumentation. The following areas are discussed: potential theory, partial differential operators of second order, Schrodinger operators, theory of convexity, one-parameter semigroups, Lie algebras, Markov processes, operator-algebras, noncommutative integration and geometry of Banach spaces.

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Table of contents :
Content:
Edited page
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages vii-viii
R. Nagel, U. Schlotterbeck, M.P.H. Wolff

List of Participants
Pages xi-xiii

Non-Linear Completely Positive Maps Original Research Article
Pages 3-13
T. Ando, M.-D. Choi

Generalizations of Self-Adjointness to Banach Spaces Original Research Article
Pages 15-25
Robert G. Bartle

Simplices in Potential Theory Original Research Article
Pages 27-39
Heinz Bauer

Spectral Properties of Some Second Order Elliptic Operators on LP-Spaces Original Research Article
Pages 41-48
E.B. Davies

Asymptotics for Bounded Semigroups on Hilbert Space Original Research Article
Pages 49-62
Jerome A. Goldstein

LP-Theory of Schrödinger Operators with a Singular Potential Original Research Article
Pages 63-78
Tosio Kato

Theory and Applications of Superconvex Spaces Original Research Article
Pages 79-118
Heinz Konig

On The Banach-Mazur Distance Between Spaces Having an Unconditional Basis Original Research Article
Pages 119-136
Joram Lindenstrauss, Andrzei Szankowski

Positive Linear Operators on LP and the Doeblin Condition Original Research Article
Pages 137-156
Heinrich P. Lotz

Local Operators, Space-Time Methods, and Evolution Equations of Diffusion Type Original Research Article
Pages 157-168
G. Lumer

Asymptotic Averages Original Research Article
Pages 169-176
W.A.J. Luxemburg

Integral Kernals and the Feynman-Kac Formalism Original Research Article
Pages 179-185
Jan A. Van Casteren

Characterization of Carleman Operators in Riesz Spaces Original Research Article
Pages 187-190
Peter van Eldik

An Ergodic Property for Certain Classes of Nonlinear Positive Operators Original Research Article
Pages 191-197
Takao Fujimoto, Ulrich Krause

Markov Semigroups and Structured Population Dynamics Original Research Article
Pages 199-208
H.J.A.M. Heijmans

Invariant Cones in Real Lie Algebras Original Research Article
Pages 209-216
Joachim Hilgert, Karl Heinrich Rofmann

Dirichlet Forms on a Measure Space Original Research Article
Pages 217-221
Francis Hirsch

Integral Representations of Stochastic Kernels Original Research Article
Pages 223-230
A. Iwanik

On Integration with Respect to a Trace Original Research Article
Pages 231-239
Michael Leinert

Generators of Positive CO -Semigroups Original Research Article
Pages 241-246
Shizuo Miyajima

Almost uniform convergence on the predual of a von Neumann algebra and an ergodic theorem Original Research Article
Pages 247-254
Dénes Petz

Spectrum-Preserving Linear Maps on the Algebra of Regular Operators Original Research Article
Pages 255-259
A.R. Sourour

An Extrapolation Theorem for the O-Spectrum Original Research Article
Pages 261-269
Lutz Weis Louisiana

Positive Operators in Reggeon Field Theory, Why? Original Research Article
Pages 271-277
Martin Zerner