Operator space

Abstract: This paper describes the Jensen-Shannon divergence (JSD) and Hilbert space embedding. With natural definitions making these considerations precise, one finds that the general Jensen-Shannon divergence related to the mixture is the minimum redundancy, which can be achieved by the observer. The set of distributions with the metric /spl radic/JSD can even be embedded isometrically into Hilbert space and the embedding can be identified.

Abstract: Generalized coherent states which are associated with a generalization of the harmonic oscillator commutation relation are investigated. It is shown that these states form an overcomplete basis in a Hilbert space of analytic functions. The generalized creation and annihilation operators are bounded except in a limit in which they reduce to the usual boson creation and annihilation operators. In this limit the Hilbert space of analytic functions reduces to the Bargmann–Segal Hilbert space of entire functions and in another limit it reduces to the Hardy–Lebesgue space.

Abstract: 0 Paradoxical decompositions 0.1 The Banach-Tarski paradox 0.2 Tarski's theorem 0.3 Notes and comments 1 Amenable, locally comact groups 1.1 Invariant means on locally compact groups 1.2 Hereditary properties 1.3 Day's fixed point theorem 1.4 Representations on Hilbert space 1.5 Notes and comments 2 Amenable Banach algebras 2.1 Johnson's theorem 2.2 Virtual and approximate diagonals 2.3 Hereditary properties 2.4 Hochschild cohomology 2.5 Notes and comments 3 Exemples of amenable Banach algebras 3.1 Banach algebras of compact operators 3.2 A commutative, radical, amenable Banach algebra 3.3 Notes and comments 4 Amenability-like properties 4.1 Super-amenability 4.2 Weak amenability 4.3 Biprojectivity and biflatness 4.4 Connes-amenability 4.5 Notes and comments 5 Banach homology 5.1 Projectivity 5.2 Resolutions and Ext-groups 5.4 Flatness and injectivity 5.4 Notes and Comments 6 C* and W*-algebras 6.1 Amenable W*-algebras 6.2 Injective W*-algebras 6.3 Tensor products of C*- and W*-algebras 6.4 Semidiscrete W*-algebras 6.5 Normal, virtual diagonals 6.6 Notes and comments 7.1 Bounded approximate identities for Fourier algebras 7.2 (Non-)amenability of Fourier 7.3 Operator amenable operator Banach algebras 7.4 Operator amenability of Fourier algebras 7.5 Operator amenability of C*-algebras 7.6 Notes and comments 8 Geometry of spaces of homomorphisms 8.1 Infinite-dimensional differential geometry 8.2 Spaces of homomorphisms 8.3 Notes and Comments Open problems A Abstract harmonic analysis A.1 Convolution of measures and functions A.2 Invariant subspaces of L(infinity symbol)(G) A.3 Regular representations on Lp(G) A.4 Notes and comments B.1 The algebraic tensor products B.2 Banach space tensor products B.2.1 The injective tensor product B.2.2 The projective tensor product B.3 The Hilbert space tensor product B.4 Notes and comments C Banach space properties C.1 Approximation properties C.2 The Radon-Nikokym property C.3 Local theory of Banach spaces C.4 Notes and comments D Operator spaces D.1 Abstract and concrete operator spaces D.2 Completely bounded maps D.3 Tensor products of operator spaces D.4 Operator Banach algebras D.5 Notes and comments List of symbols References Index