53 research outputs found
Approximations of subhomogeneous algebras
Let be a natural number. Recall that a C*-algebra is said to be
-subhomogeneous if all its irreducible representations have dimension at
most . In this short note, we give various approximation properties
characterising -subhomogeneous C*-algebras.Comment: 9 pages; v2 minor improvement in the introduction, 10 page
n-Tuples of operators satisfying σT(AB)=σT(BA)
AbstractFor “criss-cross commuting” tuples A and B of Banach space operators we give two sufficient conditions for the spectral equality σT(AB)=σT(BA)
A remark on the slice map problem
It is shown that there exist a σ-weakly closed operator algebra A˜, generated by finite rank operators and a σ-weakly closed operator algebra B˜ generated by compact operators such that the Fubini product A˜⊗¯FB˜ contains properly A˜⊗¯B˜
Numerical index and duality
We present an example of a Banach space whose numerical index is strictly
greater than the numerical index of its dual, giving a negative answer to a
question which has been latent since the beginning of the seventies. We also
show a particular case in which the numerical index of the space and the one of
its dual coincide
The group of isometries of a Banach space and duality
We construct an example of a real Banach space whose group of surjective
isometries has no uniformly continuous one-parameter semigroups, but the group
of surjective isometries of its dual contains infinitely many of them. Other
examples concerning numerical index, hermitian operators and dissipative
operators are also shown.Comment: To appear in J. Funct. Ana
Domains of commutative C*-subalgebras
A C*-algebra is determined to a great extent by the partial order of its
commutative C*-algebras. We study order-theoretic properties of this dcpo. Many
properties coincide: the dcpo is, equivalently, algebraic, continuous,
meet-continuous, atomistic, quasi-algebraic, or quasi-continuous, if and only
if the C*-algebra is scattered. For C*-algebras with enough projections, these
properties are equivalent to finite-dimensionality. Approximately
finite-dimensional elements of the dcpo correspond to Boolean subalgebras of
the projections of the C*-algebra, which determine the projections up to
isomorphism. Scattered C*-algebras are finite-dimensional if and only if their
dcpo is Lawson-scattered. General C*-algebras are finite-dimensional if and
only if their dcpo is order-scattered.Comment: 42 page
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