Let M be a II (1)-factor with trace tau, the finite dimensional subspaces of L (2)(M, tau) are not just common Hilbert spaces, but they have an additional structure. We introduce the notion of a cyclic linear space by taking these additional properties as axioms. In Sect. 3 we formulate the following problem: "does every cyclic Hilbert space embed into L (2)(M, tau), for some M?". An affirmative answer would imply the existence of an algorithm to check Connes' embedding Conjecture. In Sect. 4 we make a first step towards the answer of the previous question.

Capraro, V., & Radulescu, F. (2013). Cyclic Hilbert Spaces and Connes' Embedding Problem. COMPLEX ANALYSIS AND OPERATOR THEORY, 7(4), 863-872 [10.1007/s11785-011-0188-4].

Cyclic Hilbert Spaces and Connes' Embedding Problem

RADULESCU, FLORIN
2013

Abstract

Let M be a II (1)-factor with trace tau, the finite dimensional subspaces of L (2)(M, tau) are not just common Hilbert spaces, but they have an additional structure. We introduce the notion of a cyclic linear space by taking these additional properties as axioms. In Sect. 3 we formulate the following problem: "does every cyclic Hilbert space embed into L (2)(M, tau), for some M?". An affirmative answer would imply the existence of an algorithm to check Connes' embedding Conjecture. In Sect. 4 we make a first step towards the answer of the previous question.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Connes Embedding Probplem
Capraro, V., & Radulescu, F. (2013). Cyclic Hilbert Spaces and Connes' Embedding Problem. COMPLEX ANALYSIS AND OPERATOR THEORY, 7(4), 863-872 [10.1007/s11785-011-0188-4].
Capraro, V; Radulescu, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/90217
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