7,229 research outputs found
Representable and continuous functionals on Banach quasi *-algebras
In the study of locally convex quasi *-algebras an important role is played
by representable linear functionals; i.e., functionals which allow a
GNS-construction. This paper is mainly devoted to the study of the continuity
of representable functionals in Banach and Hilbert quasi *-algebras. Some other
concepts related to representable functionals (full-representability,
*-semisimplicity, etc) are revisited in these special cases. In particular, in
the case of Hilbert quasi *-algebras, which are shown to be fully
representable, the existence of a 1-1 correspondence between positive, bounded
elements (defined in an appropriate way) and continuous representable
functionals is proved
Algebras and universal quantum computations with higher dimensional systems
Here is discussed application of the Weyl pair to construction of universal
set of quantum gates for high-dimensional quantum system. An application of Lie
algebras (Hamiltonians) for construction of universal gates is revisited first.
It is shown next, how for quantum computation with qubits can be used
two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford
algebras, and discussed well known applications to product operator formalism
in NMR, Jordan-Wigner construction in fermionic quantum computations. It is
introduced universal set of quantum gates for higher dimensional system
(``qudit''), as some generalization of these models. Finally it is briefly
mentioned possible application of such algebraic methods to design of quantum
processors (programmable gates arrays) and discussed generalization to quantum
computation with continuous variables.Comment: 12 pages, LaTeXe, Was prepared for QI2002, Moscow, 1-4.1
Equivariant property (SI) revisited
We revisit Matui-Sato's notion of property (SI) for C*-algebras and
C*-dynamics. More specifically, we generalize the known framework to the case
of C*-algebras with possibly unbounded traces. The novelty of this approach
lies in the equivariant context, where none of the previous work allows one to
(directly) apply such methods to actions of amenable groups on highly
non-unital C*-algebras, in particular to establish equivariant Jiang-Su
stability. Our main result is an extension of an observation by Sato: For any
countable amenable group and any non-elementary separable simple
nuclear C*-algebra with strict comparison, every -action on has
equivariant property (SI). A more general statement involving relative property
(SI) for inclusions into ultraproducts is proved as well. As a consequence we
show that if also has finitely many rays of extremal traces, then every
-action on is equivariantly Jiang-Su stable. We moreover provide
applications of the main result to the context of strongly outer actions, such
as a generalization of Nawata's classification of strongly outer automorphisms
on the (stabilized) Razak-Jacelon algebra.Comment: v4 36 pages; this version has been accepted at Analysis & PD
Bohr's inequality revisited
We survey several significant results on the Bohr inequality and presented
its generalizations in some new approaches. These are some Bohr type
inequalities of Hilbert space operators related to the matrix order and the
Jensen inequality. An eigenvalue extension of Bohr's inequality is discussed as
well.Comment: 13 pages, to appear in a Springer volume edited by P. Pardalos, H.M.
Srivastava, and P. Georgie
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