Riesz spaces Vol. 1 / W. A. J. Luxemburg and A. C. Zaanen.

• Ch. 1 Distributive Lattices and Normed Function Spaces -- Ch. 2 Elementary Properties of Ordered Vector Spaces and Riesz Spaces -- Ch. 3 Ideals and Bands; Archimedean Riesz Spaces -- Ch. 4 Dedekind Completeness and Projection Properties -- Ch. 5 Prime Ideals -- Ch. 6 Freudenthal's Spectral Theorem -- Ch. 7 Spectral Representation Theory -- Ch. 8 Hermitian Operators in Hilbert Space -- Ch. 9 Riesz Homomorphisms and Quotient Spaces -- Ch. 10 The Egoroff Property and the Diagonal Property. 

• The present volume is devoted mainly to the algebraic aspects of the subject. Volume II will emphasize the functional analytic aspects. Important topics covered are Freudenthal's spectral theorem (with applications to spectral theory in Hilbert space), the theory of prime ideals in Riesz spaces and the corresponding spectral representation theory - several versions of which are discussed. 

Ämnesord

Riesz spaces  (LCSH)

Funktionsanalys 

Indexterm och SAB-rubrik

Tdg Funktionalanalys

Tdg Funktionalanalys

Klassifikation

517.5(021) (UDK)

513.88(021) (UDK)

515/.73 (DDC)

46A40 (msc)

06F20 (msc)

Tdg (kssb/6)