Functional analysis. Textbook. (Funktsional’nyj analiz. Uchebnoe posobie). (Russian) Zbl 0517.46001

Trenogin, V. A.

Moskva: “Nauka”. 495 p. R. 1.30 (1980).

MSC:

46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
46B10	Duality and reflexivity in normed linear and Banach spaces
47-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
46G05	Derivatives of functions in infinite-dimensional spaces
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
58-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis
65J05	General theory of numerical analysis in abstract spaces
47H10	Fixed-point theorems
58C15	Implicit function theorems; global Newton methods on manifolds

Keywords:

Banach spaces; Lebesgue and Sobolev spaces; method of the small parameter; method of parametric extension; conjugate spaces; Hahn-Banach theorem; compact sets; completely continuous operators; normally solvable operators; Fredholm theory; spectral theory of linear operators; selfadjoint operators; approximate solution; abstract approximation schemes; fixed points of nonlinear operators; Frechet and Gateaux differentials; abstract implicit function theorem; monotone coercive and demicontinuous operators; Fatou theorem; adjoint operator