Mariusz Wodzicki

Commutator structure of operator ideals

Commutator structure of operator ideals Ken Dykema, ,1 Tadeusz Figiel, Gary Weiss, and Mariusz Wodzicki Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA b Instytut Matematyczny Polskiej Akademii Nauk, 81-825 Sopot, Poland Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA

Excision in algebraic K-theory

Introduction 1. Excision and the homology of affine groups 2. Volodins spaces 3. Excision for rings with the Triple Factorization Property 4. Lie analogue of Volodins construction 5. The homology of nilpotent groups and nilpotent Lie algebras 6. A proof of the main theorems 7. The tensor product of H-unital algebras 8. The matrix ring of a small category 9. The acyclicity of triangular complexes 10. A proof of Karoubis Conjecture

Algebraic K-Theory and Functional Analysis

Around 1978 Max Karoubi made a striking conjecture about the K-theory of Banach algebras. His conjecture predicted that the topological K-groups K * top(B) of a unital Banach algebra B were isomorphic to the algebraic K-groups K *(B⊗r)C) of the Grothendieck’s projective tensor product of B and the ideal K of compact operators on the standard Hilbert space H = l2 (ℕ). Notice that B⊗K, is a norm completion of the matrix algebra M ∞(B) = B ⊗ M ∞(ℂ) and K *(M ∞(B)) = K *(B).

Unitarily invariant trace extensions beyond the trace class

The existence of unitarily invariant trace extensions of the standard trace on the ideal of finite rank operators in B(H) past the trace class to a strictly larger ideal is proven using matrix forms and a certain commutator trace obstruction.

Elliptic Curves with Large Analytic Order of Ш(E)

We present the results of our search for elliptic curves over \(\mathbb{Q}\) with exceptionally large analytic orders of the Tate-Shafarevich group. We exibit \(134\) examples of rank zero curves with | Open image in new window E| > 18322 which was the largest known value for any explicit curve. Our record is a curve with Open image in new window .