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Weak amenability of triangular Banach algebras
Let A and B be unital Banach algebras, and let M be a Banach A, B-module. Then T = [ A M 0 B ] becomes a triangular Banach algebra when equipped with the Banach space norm || [ a m 0 b ] || = ||a|| AExpand
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On the linear span of the projections in certain simple C*-algebras
In this paper we show that if a C*-algebra A admits a certain 3 × 3 matrix decomposition, then every commutator in A can be written as a linear combination of at most 84 projections in A. In certainExpand
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LIE ISOMORPHISMS OF NEST ALGEBRAS
Abstract In this paper we characterize linear maps ϕ between two nest algebras T ( N ) and T ( M ) which satisfy the property that ϕ ( AB − BA )= ϕ ( A )  ϕ ( B )− ϕ ( B )  ϕ ( A ) for all A ,  B ∈ TExpand
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Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras
Abstract In this article we classify linear maps ϕ from the algebra T n of n × ? upper triangular matrices into itself satisfying ϕ(ab − ba) = 0 if and only if ab − ba = 0. In particular, we showExpand
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Abelian, amenable operator algebras are similar to C∗ -algebras
Suppose that H is a complex Hilbert space and that B(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C*-algebra. We do this byExpand
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Unitarily-invariant linear spaces in C*-algebras
Characterisations and containment results are given for linear subspaces of a unital C*-algebra that are invariant under conjugation by sets of unitary elements of the algebra. TheExpand
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PROJECTIONS, COMMUTATORS AND LIE IDEALS IN C * -ALGEBRAS
In this expository note, we survey some recent investigations into the problem of determining when the (algebraic) linear span of the projections in a unital, simple C*-algebra A coincides with theExpand
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Triangularizability of operators with increasing spectrum
We establish finite- and infinite-dimensional versions of the following assertion. If M is a matrix with the property that whenever P and Q are diagonal projections with P⩽Q, the spectrum of PMPExpand
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