Undergraduate seminars on operator algebras

Progress

• Feb 09 by Yamashita
  • Correspondence between the closed ideals and the w*-closed unitary invariant subsets of P(A)
  • Commutative C*-algebras are nuclear
  • Normal homomorphisms between W*-algebras
  • Decomposition of normal homomorphisms by amplification and induction
• Feb 09 by Zhang
  • Positive normal functionals
• Jan 30 by Ogawa
  • Completely positive maps
  • Spacial implementation of completely positive maps over separable C*-algebras
• Jan 27 by Zhang
  • Polar decomposition of μ-continuous functionals
  • Decomposition of functionals over C*-algebras
• Jan 27 by Mimura
  • Up & down theorem (second part)
• Jan 23 by Tanimoto
  • Weak approximate unitary equivalence
  • Characterization of the unitary equivalence of representations
• Jan 20 by Mimura
  • Unitary version of the noncommutative Lusin's theorem
  • Up & down theorem (first part)
• Jan 16 by Sakiyama
  • Approximation of normal operators by diagonalizable ones
  • Approximate unitary equivalence
• Jan 13 by Yamashita
  • Tensor product of representations
  • Irreducibility of the tensor product of representations
  • Injective C*-tensor product of C*-algebras
  • Faithful representation of the injective C*-tensor products
  • Decomposition of the irreducible representations of A ⊗ B when A is commutative
• Dec 19 by Tanimoto
  • Commutative von Neumann algebras have sufficiently many projections that have uniform multiplicities
  • Fredholm operators
  • Essential spectra of Fredholm operators
• Dec 16 by Yamashita
  • Tensor product of Hilbert spaces
• Dec 16 by Zhang
  • Uniqunese of predual of W*-algebras
• Dec 12 by Sakiyama
  • Uniform multiplicity of abelian von Neumann algebras
• Dec 09 by Zhang
  • Sakai's theorem: any projection of norm one for B ↪ A is B-bilinear
  • A is a W*-algebra when it is isomorphic to the dual of some Banach space
• Dec 05 by Ogawa
  • Equivalence of abelian von Neumann algebras and L^∞(μ)s
• Nov 28 by Tanimoto
  • Unitary equivalence
  • Unitary equivalence of cyclic representations
• Nov 21 by Sakiyama
  • Minimal projections
  • Irreducible representations of subalgebras of K(H)
  • Unitary equivalence of representations
  • Uniquness of irreducible representation of K(H)
  • Decomposition of representations
• Nov 18 by Mimura
  • Equivalence of topologies of the space of normal elements in B(H)
  • Noncommutative measurable space theory (Egorov's and Lusin's theorems)
• Nov 16 by Ogawa
  • Semisimplicity of C*-algebras
  • Extension of representations of ideals
• Nov 11 by Yamashita
  • Weak operator closed *algebras are unital
  • Bimodules over von Neumann algebras
  • Normal and singular functionals
• Nov 11 by Mimura
  • The theorem of Kreǐn-Smul'yan
• Nov 09 by Tanimoto
  • Irreducible representations
  • Pure states
  • Jordan decomposition of Hermitian functionals
• Nov 04 by Yamashita
  • Universal enveloping von-Neumann algebras
• Nov 04 by Mimura
  • Complements for the Oct 28 talk
• Oct 31 by Sakiyama
  • Stone-Weierstrasse for locally compact spaces
  • Strongly continuous functions in one real variable
  • Density propositions in the unit ball
• Oct 28 by Mimura
  • strong*, σ-strong, and σ-strong* topologies on B(H)
  • Equivalence of the foo topology and the σ-foo topology on the unit ball (foo = weak (op), strong (op) or strong*)
  • Induced algebra and reduced algebra with respect to a projection in a von-Neumann algebra
• Oct 19 by Yamashita
  • Isomorphism between K(H)* and the projective tensor product H* ⊗ H
  • σ-weak topology on B(H)
  • E = E_** for σ-weakly closed subspace E of B(H)
• Oct 17 by Tanimoto
  • ideals and quotients of C*-algebras
  • strong and weak operator topologies; continuity, metrizability and representation of continuous linear functionals
• Oct 3 by Sakiyama
  • Unitization of non-unital C*-algebras
  • Approximate identities