Functional analysis. Transl. from the Russian by Howard L. Silcock. 2nd ed. (English) Zbl 0484.46003

Kantorovich, L. V.; Akilov, G. P.

Oxford etc.: Pergamon Press. xiv, 589 p. hbk: £45.00; $ 100.00; pbk: £10.00; $ 25.00 (1982).

The book is divided into two parts. Part I is devoted to linear operators and functionals. Part II deals with functional equations.
In this second edition, the entire exposition is based on the theory of topological vector spaces. Ideal spaces of measurable functions form a foundation on which the theory of integral operators and their representations is constructed. Additional material includes partially ordered spaces, topics connected with mathematical economics and control theory, and a modified list of books and papers on topics in functional analysis.
This book can be a source-book or a text at graduate level course, using [N. Dunford and J. Schwartz, Linear Operators (three volumes). (1958; Zbl 0084.10402), (1963; Zbl 0128.34803), (1973; Zbl 0243.47001)] as reference. The set-up is excellent.

Reviewer: K. Chandrasekharo Rao

MSC:

46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
46B03	Isomorphic theory (including renorming) of Banach spaces
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47A50	Equations and inequalities involving linear operators, with vector unknowns
46B10	Duality and reflexivity in normed linear and Banach spaces
47Gxx	Integral, integro-differential, and pseudodifferential operators

Keywords:

linear operators and functionals; functional equations; ideal spaces of measurable functions; integral operators; partially ordered spaces; mathematical economics; control theory