دانلود کتاب A Course in Commutative Banach Algebras

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Preface
Contents
General Theory of Banach Algebras
Basic definitions and examples
The spectrum of a Banach algebra element
L1-algebras and Beurling algebras
Ideals and multiplier algebras
Tensor products of Banach algebras
Exercises
Notes and references
Gelfand Theory
Multiplicative linear functionals
The Gelfand representation
Finitely generated commutative Banach algebras
Commutative C-algebras
The uniform algebras P(X) and R(X)
The structure space of A(X)
The Gelfand representation of L1(G)
Beurling algebras L1(G,)
The Fourier algebra of a locally compact group
The algebra of almost periodic functions
Structure spaces of tensor products
Exercises
Notes and references
Functional Calculus, Shilov Boundary, and Applications
The holomorphic functional calculus
Some applications of the functional calculus
The Shilov boundary
Topological divisors of zero
Shilov\'s idempotent theorem and applications
Exercises
Notes and references
Regularity and Related Properties
The hull-kernel topology
Regular commutative Banach algebras
The greatest regular subalgebra
Regularity of L1(G)
Spectral extension properties
The unique uniform norm property
Regularity of Beurling algebras
Exercises
Notes and references
Spectral Synthesis and Ideal Theory
Basic notions and local membership
Spectral sets and Ditkin sets
Ideals in Cn[0,1]
Spectral synthesis in the Mirkil algebra
Spectral sets and Ditkin sets for L1(G)
Ideals with bounded approximate identities in L1(G)
On spectral synthesis in projective tensor products
Exercises
Notes and references
Appendix
Topology
Functional analysis
Measure and integration
Haar measure and convolution on locally compact groups
The Pontryagin duality theorem
The coset ring of an Abelian group
References
Index