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A Note on Free Quantum Groups

Teodor Banica (2008)

Annales mathématiques Blaise Pascal

We study the free complexification operation for compact quantum groups, G → G c . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying G = G c .

A note on local automorphisms

Ajda Fošner (2006)

Czechoslovak Mathematical Journal

Let H be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ℬ ( H ) , the algebra of all bounded linear operators on a Hilbert space H , is an automorphism.

A Note on L-sets

Gero Fendler (2002)

Colloquium Mathematicae

Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.

A note on normal generation and generation of groups

Andreas Thom (2015)

Communications in Mathematics

In this note we study sets of normal generators of finitely presented residually p -finite groups. We show that if an infinite, finitely presented, residually p -finite group G is normally generated by g 1 , ⋯ , g k with order n 1 , ⋯ , n k ∈ { 1 , 2 , ⋯ } ∪ { ∞ } , then β 1 ( 2 ) ( G ) ≤ k - 1 - ∑ i = 1 k 1 n i , where β 1 ( 2 ) ( G ) denotes the first ℓ 2 -Betti number of G . We also show that any k -generated group with β 1 ( 2 ) ( G ) ≥ k - 1 - ε must have girth greater than or equal 1 / ε .

A note on regular elements in Calkin algebras.

Vladimir Rakocevic (1992)

Collectanea Mathematica

An element a of the Banach algebra A is said to be regular provided there is an element b belonging to A such that a = aba. In this note we study the set of regular elements in the Calkin algebra C(X) over an infinite-dimensional complex Banach space X.

A note on states of von Neumann algebras

Allah-Bakhsh Thaheem (1979)

Aplikace matematiky

The author proves that on a von Neumann albebra (possibly of uncountable cardinality) there exists a family of states having mutually orthogonal supports (projections) converging to the identity operator.

Currently displaying 61 – 80 of 190