5 edition of Locally convex spaces and operator ideals. found in the catalog.
Abstracts in French, German and Russian.
|The Physical Object|
|Pagination||xvi, 104 p. :|
|Number of Pages||47|
|2||Teubner-Texte zur Mathematik -- Bd 56|
nodata File Size: 7MB.
The index formula for Toeplitz operators. Relations between kernels and images of operators and of their duals. Corollaries: Johnson's lemma on exact sequences of Banach spaces; the Fredholm property and the index of the dual operator.
2021 The domination relation for families of seminorms. 2021 Equicontinuous families of linear operators. The continuity criterion for a linear operator between locally convex spaces.
Toeplitz operators on the Hardy space. 2021 A survey of compact metric spaces. The maximal spectrum and the character space of a commutative unital algebra. The correspondence between finitely additive spectral measures and representations of B A X.
Nikolski's characterization of Fredholm operators of index zero. A characterization of reflexive Banach spaces in terms of topologies on the dual.
The 1st commutative Gelfand-Naimark theorem. The correspondence between regular spectral measures and WMT-WOT-continuous representations of B X. Corollaries: the closure of a vector subspace equals the weak closure; a density criterion for a vector subspace; relations between kernels and images of a linear operator and of the dual operator.
If you solve such exercises, you will earn bonus points. The essential spectrum of a linear operator. The stability of the index under compact perturbations. A duality between isometries and coisometries on Banach spaces. A corollary: the spectral decomposition of a normal operator Spectral Theorem III.
2021 The adjoint of an operator between Hilbert spaces. The spectrum of a selfadjoint operator is real. A corollary: the existence of the Borel functional calculus for a normal operator. Compact operators: definition, simplest examples and counterexamples.
Dual pairs of vector spaces.
Toeplitz operators on the Hardy space.
The correspondence between finitely additive spectral measures and representations of B A X.
The Nikolski-Atkinson criterion for Fredholm operators.
Remarks on the approximation property and Schauder bases.