Wyniki wyszukiwania

1

Notes on automorphisms of ultrapowers of II₁ factors

100%

Sherman D.

Studia Mathematica

|

2009

|

tom 195

|

nr 3

201-217

EN

In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II₁ factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is ℵ₀-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a separable nuclear C*-algebra into an ultrapower of a II₁ factor, equality of the induced traces implies unitary equivalence. All statements are proved using operator-algebraic techniques, but in the last section of the paper we indicate how the underlying principle is related to theorems of Henson's positive bounded logic.

2

A new proof of the noncommutative Banach-Stone theorem

100%

Sherman D.

Banach Center Publications

|

2006

|

tom 73

|

nr 1

363-375

EN

Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison's theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate how our techniques may be applied to classify surjective isometries of noncommutative $L^p$ spaces, extending the main results of [S1] to 0 < p ≤ 1.

3

Existentially closed II₁ factors

51%

Farah I., Goldbring I., Hart B., Sherman D.

Fundamenta Mathematicae

|

2016

|

tom 233

|

nr 2

173-196

EN

We examine the properties of existentially closed ($𝓡 ^{ω}$-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ($𝓡 ^{ω}$-embeddable) II₁ factor is approximately inner to prove that Th(𝓡) is not model-complete. We also show that Th(𝓡) is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th(𝓡).

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

1 Studia Mathematica

3 Sherman D.

1 Farah I.

1 Goldbring I.

1 Hart B.

1 2016

1 2009

1 2006

Notes on automorphisms of ultrapowers of II₁ factors

A new proof of the noncommutative Banach-Stone theorem

Existentially closed II₁ factors