共查询到20条相似文献,搜索用时 31 毫秒
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.
Wolfgang Rump 《Archiv der Mathematik》2007,89(2):131-142
We introduce one-sided thick subcategories
of an arbitrary preadditive category
and define a quotient category
. When
is abelian, this concept specializes to Grothendieck’s quotient for two-sided thick
. We determine the left noetherian rings for which the injective modules form a left thick subcategory. We exhibit a class
of one-sided thick subcategories in categories of coherent functors which are ubiquitous in representation theory.
Received: 14 November 2006 Revised: 12 March 2007 相似文献
3.
Alejandra Maestripieri Francisco Martínez Pería 《Integral Equations and Operator Theory》2007,59(2):207-221
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded)
J-selfadjoint operator A (with the unique factorization property) acting on a Krein space
and a suitable closed subspace
of
, the Schur complement
of A to
is defined. The basic properties of
are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive
operators on a Hilbert space.
To the memory of Professor Mischa Cotlar 相似文献
4.
Hyoung Joon Kim 《Integral Equations and Operator Theory》2008,61(1):103-120
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q
*
Q has an infinite dimensional reducing subspace M with Q
*
Q|
M
compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus
it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial
solutions to the hyperinvariant subspace problem.
相似文献
5.
Yonutz V. Stanchescu 《Combinatorica》2008,28(3):343-355
We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ3 such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity
υ or by increasing the upper bounds for . 相似文献
6.
Lorenz J. Schwachhöfer 《Archiv der Mathematik》2008,90(2):158-162
We show that a left invariant metric on a compact Lie group G with Lie algebra has some negative sectional curvature if it is obtained by enlarging a biinvariant metric on a subalgebra , unless the semi-simple part of is an ideal of This answers a question raised in [8].
Received: 7 May 2007 相似文献
7.
F. E. A. Johnson 《Archiv der Mathematik》2008,90(2):123-132
A module J over a ring is said to be hyperstable when . Over a module M for which Ext we show that the projective n-stems for which is hyperstable constitute a single homotopy type.
Received: 17 November 2006 相似文献
8.
M. Amélia Bastos Claudio A. Fernandes Yuri I. Karlovich 《Complex Analysis and Operator Theory》2008,2(2):241-272
The C*-subalgebra of generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular
integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms with any nonempty set of common fixed points is studied. A symbol calculus for the C*-algebra and a Fredholm criterion for its elements are obtained. For the C*-algebra composed by all functional operators in , an invertibility criterion for its elements is also established. Both the C*-algebras and are investigated by using a generalization of the local-trajectory method for C*-algebras associated with C*-dynamical systems which is based on the notion of spectral measure.
Submitted: April 30, 2007. Accepted: November 5, 2007. 相似文献
9.
Christian Dzierzon 《Applied Categorical Structures》2006,14(1):63-80
This paper presents a general construction, defining for each given strong generator in any locally finitely presentable category an essentially algebraic, finitary theory – maximal in a certain sense – such that is equivalent to the category of models of . For regular generators , generalization to the non-finitary case is easily done, and yields a new proof of the famous characterization of many-sorted
quasivarieties. 相似文献
10.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
11.
Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:
(ws) if , then x is weakly separated from G;
(ps) if , then x is -separated from G;
(wp) if Tx is -separated from T(G), then x is weakly separated from G.
By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .
相似文献
12.
Amol Sasane 《Complex Analysis and Operator Theory》2009,3(1):323-330
Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite.
Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007. 相似文献
13.
In this paper, we compute certain invariants of extension algebras of the torus algebra by , where is the C*-algebra of compact operators on an infinite dimensional separable Hilbert space H. These extension algebras are also constructed up to isomorphism.
Received: 5 July 2007, Revised: 14 February 2008 相似文献
14.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2008,151(2):2907-2923
New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists Abelian factors (“rotations”) , and sets of quasi-Jordanian twists . The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra for the composition is a nonminimal parabolic subalgebra in A
n−1 such that . The parabolic twisting elements are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11.
Bibliography: 21 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 187–213. 相似文献
15.
Morton E. Harris 《Results in Mathematics》2008,51(3-4):249-259
As in Finite Group Modular Representation Theory, let be a commutative complete noetherian ring with an algebraically closed residue field k. Let G be a finite group and let N be a normal subgroup of G. First suppose that V is an indecomposable -module, so that Inf
G
G/N
(V) is an indecomposable G-module. We relate the Green invariants of V as an -module to those of Inf
G
G/N
(V) as an G-module. Secondly, let V and W be indecomposable G-modules. Assume that W is an endo-permutation lattice and that is also an indecomposable G-module. We relate the Green invariants of the G-modules V and . (This situation arises under important Morita equivalences.)
Received: December 11, 2006. Revised: August 22, 2007. 相似文献
16.
The C
*-algebra
generated by the n poly-Bergman and m antipoly-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space
L
2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky
results on two-dimensional convolution operators with symbols admitting homogeneous discontinuities we reduce the study to
simpler C
*-algebras associated with points
and pairs
. Applying a symbol calculus for the abstract unital C
*-algebras generated by N orthogonal projections sum of which equals the unit and by M = n + m one-dimensional orthogonal projections and using relations for the Gauss hypergeometric function, we study local algebras
at points
being the discontinuity points of coefficients. A symbol calculus for the C
*-algebra
is constructed and a Fredholm criterion for the operators
is obtained. 相似文献
17.
Michel Weber 《Results in Mathematics》2007,51(1-2):141-179
Let where are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic
order of the sums , where and is a sequence of positive integers.
Received: May 23, 2007. Revised: June 8, 2007. 相似文献
18.
Xavier Mary 《Integral Equations and Operator Theory》2008,60(3):419-433
We discuss the notion of Moore-Penrose inverse in Kreĭn spaces for both bounded and unbounded operators. Conditions for the
existence of a Moore-Penrose inverse are given. We then investigate its relation with adjoint operators, and study the involutive
Banach algebra . Finally applications to the Schur complement are given.
相似文献
19.
Let be a smooth continuous trace algebra, with a Riemannian manifold spectrum X, equipped with a smooth action by a discrete group G such that G acts on X properly and isometrically. Then is KK-theoretically Poincaré dual to , where is the inverse of in the Brauer group of Morita equivalence classes of continuous trace algebras equipped with a group action. We deduce this
from a strengthening of Kasparov’s duality theorem. As applications we obtain a version of the above Poincaré duality with
X replaced by a compact G-manifold M and Poincaré dualities for twisted group algebras if the group satisfies some additional properties related to the Dirac
dual-Dirac method for the Baum- Connes conjecture.
This research was supported by the EU-Network Quantum Spaces and Noncommutative Geometry (Contract HPRN-CT-2002-00280) and the Deutsche Forschungsgemeinschaft (SFB 478) and by the National Science and Engineering Research Council of Canada Discovery Grant program. 相似文献
20.
In the first part [16] of this work, we described the commutative C*-algebras generated by Toeplitz operators on the unit ball whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of . Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of
the unit disk (see [3]) admits a natural generalization to the unit ball . Furthermore we give a classification result for commutative Toeplitz operator C*-algebras in terms of geometric and “dynamic” properties of the level sets of generating symbols.
This work was partially supported by CONACYT Projects 46936 and 44620, México. 相似文献