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1.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
2.
Let
be a C*-algebra. We obtain some conditions that are equivalent to the statement that every n-positive elementary operator on
is completely positive. 相似文献
3.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φx of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
4.
5.
Carlos E. Durán Luis E. Mata-Lorenzo Lázaro Recht 《Integral Equations and Operator Theory》2005,53(1):33-50
This article focuses on the study of the metric geometry of homogeneous spaces
(the unitary group of a C*-algebra
modulo the unitary group of a C*-subalgebra
) where the invariant Finsler metric in
is induced by the quotient norm of
Under the assumption that
is of compact type, i.e. when the unitary group is relatively compact in the strong operator topology, this work presents local and global versions of Hopf-Rinow-like theorems: given points
there exists a minimal uniparametric group curve joining ρ0 and ρ1. 相似文献
6.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
7.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
8.
Vasily A. Prokhorov Edward B. Saff Maxim Yattselev 《Complex Analysis and Operator Theory》2009,3(2):501-524
Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:
where is the supremum norm on a compact set K, is the set of all algebraic polynomials of degree at most m, and as . Subsequently, we obtain asymptotic behavior of the Kolmogorov k-widths, , of the unit ball An∞ of restricted to E in C(E), where H∞ is the Hardy space of bounded analytic functions on G and C(E) is the space of continuous functions on E.
Received: April 24, 2008. Accepted: May 15, 2008. 相似文献
9.
M. A. Bastos C. A. Fernandes Yu. I. Karlovich 《Integral Equations and Operator Theory》2006,55(1):19-67
We establish a symbol calculus for the C*-subalgebra
of
generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators
where
is the Cauchy singular integral operator and
The C*-algebra
is invariant under the transformations
where Uz is the rotation operator
Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type
operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra
generated by the operators
and
for the C*-algebra
generated by the operators
and
and for the C*-algebra
generated by the algebras
and
The C*-algebra
can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting
freely. 相似文献
10.
For an arbitrary set E and a given closure operator
, we want to construct a symmetric closure operator
via some – possibly infinite – iteration process. If E is finite, the corresponding symmetric closure operator .
defines a matroid. If
and
is the convex closure operator,
turns out to be the affine closure operator. Moreover, we apply the symmetrization process to closure operators induced by
visibility.
Received March 9, 2005 相似文献
11.
Evgueni Doubtsov 《Integral Equations and Operator Theory》2009,64(2):177-192
Let Bn denote the unit ball of , n ≥ 2. Given an α > 0, let denote the class of functions defined for by integrating the kernel against a complex-valued measure on the sphere . Let denote the space of holomorphic functions in the ball. A function is called a multiplier of provided that for every . In the present paper, we obtain explicit analytic conditions on which imply that g is a multiplier of . Also, we discuss the sharpness of the results obtained.
This research was supported by RFBR (grant no. 08-01-00358-a), by the Russian Science Support Foundation and by the programme
“Key scientific schools NS 2409.2008.1”. 相似文献
12.
Christian Richter 《Journal of Geometry》2006,84(1-2):117-132
Let
be a group of affine transformations of the Euclidean plane
. Two topological discs D,
are called congruent by dissection with respect to
if D can be dissected into a finite number of subdiscs that can be rearranged by maps from
to a dissection of E.
Our main result says in particular that
admits congruence by dissection of any circular disc C with any square S if and only if
contains a contractive map and all orbits
,
, are dense in
. In this case any two discs D and E are congruent by dissection with respect to
and every disc D is congruent by dissection with n copies of D for every n ≥ 2.
Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection.
Dedicated to Irmtraud Stephani on the occasion of her 70th birthday 相似文献
13.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
14.
Maribel Loaiza 《Integral Equations and Operator Theory》2005,51(1):141-153
Let
and
be a finite collection of smooth curves in D. Given k points
consider the family
of all bounded and continuous functions on
with finite limits at
and radial limits at zk. We study the Toeplitz operator algebra
corresponding to Mr and we prove that its Calkin algebra is isomorphic to the algebra of all continuous functions on some compact set. This fact implies that the commutator of two Toeplitz operators with this kind of symbols is compact. We also prove that the semi-commutator of such Toeplitz operators is not compact, in general. 相似文献
15.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
16.
We consider logarithmic connections, on rank n and degree d vector bundles over a compact Riemann surface X, singular over a fixed point x0 ∈ X with residue in the center of
the integers n and d are assumed to be mutually coprime. A necessary and sufficient condition is given for a vector bundle to admit such a logarithmic
connection. We also compute the Picard group of the moduli space of all such logarithmic connections. Let
denote the moduli space of all such logarithmic connections, with the underlying vector bundle being of fixed determinant
L, and inducing a fixed logarithmic connection on the determinant line L. Let
be the Zariski open dense subset parametrizing all connections such that the underlying vector bundle is stable. The space
of all global sections of certain line bundles on
are computed. In particular, there are no nonconstant algebraic functions on
Therefore, there are no nonconstant algebraic functions on
although
is biholomorphic to a representation space which admits nonconstant algebraic functions. The moduli space
admits a natural compactification by a smooth divisor. We investigate numerically effectiveness of this divisor at infinity.
It turns out that the divisor is not numerically effective in general.
Received: March 2004 Revision: May 2004 Accepted: May 2004 相似文献
17.
For an l-graph
, the Turán number
is the maximum number of edges in an n-vertex l-graph
containing no copy of
. The limit
is known to exist [8]. The Ramsey–Turán density
is defined similarly to
except that we restrict to only those
with independence number o(n). A result of Erdős and Sós [3] states that
as long as for every edge E of
there is another edge E′of
for which |E∩E′|≥2. Therefore a natural question is whether there exists
for which
.
Another variant
proposed in [3] requires the stronger condition that every set of vertices of
of size at least εn (0<ε<1) has density bounded below by some threshold. By definition,
for every
. However, even
is not known for very many l-graphs
when l>2.
We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we
construct, for each l≥3, infinitely many l-graphs
for which
.
We also prove that the 3-graph
with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies
. The existence of a hypergraph
satisfying
was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based
on different ideas and is simpler than these earlier proofs.
* Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P.
Sloan Research Fellowship.
† Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529. 相似文献
18.
Takao Watanabe 《Archiv der Mathematik》2006,87(4):320-329
Let V be a vector space over a global field k, g an element of the adele group
and Hg the twisted height defined on the k-subspaces of V . We show that the square root of the generalized Hermite-Rankin constant for k gives the best upper bound of the function
, where
runs over all m-dimensional k-subspaces of V and
runs over all n-dimensional k-subspaces of
.
Received: 17 June 2005 相似文献
19.
Let
be a family of unit balls in
with the property that the mutual distances of the centers are at least
. If any n2 members of
have a common line transversal, then
has a line transversal too.
Received: 27 January 2005; revised: 17 October 2005 相似文献
20.
For a discrete group G, we prove that a G-map between proper G–CW-complexes induces an isomorphism in G-equivariant K-homology if it induces an isomorphism in C-equivariant K-homology for every finite cyclic subgroup C of G. As an application, we show that the source of the Baum–Connes assembly map, namely K
*
G
(E(G,
in)), is isomorphic to K
*
G
(E(G,
)), where E(G,
) denotes the classifying space for the family of finite cyclic subgroups of G. Letting
be the family of virtually cyclic subgroups of G, we also establish that and related results. 相似文献