共查询到20条相似文献,搜索用时 18 毫秒
1.
N. L. Vasilevski 《Integral Equations and Operator Theory》1999,34(1):107-126
Let
be the unit disk in,
be the Bergman space, consisting of all analytic functions from
, and
be the Bergman projection of
onto
. We constructC
*-algebras
, for functions of which the commutator of Toeplitz operators [T
a
,T
b
]=T
a
T
b
–T
b
T
a
is compact, and, at the same time, the semi-commutator [T
a
,T
b
)=T
a
T
b
–T
ab
is not compact.It is proved, that for each finite set =n
0,n
1, ...,n
m
, where 1=n
0
1
<...
m
, andn
k
{}, there are algebras
of the above type, such that the symbol algebras Sym
of Toeplitz operator algebras
arecommutative, while the symbol algebras Sym
of the algebras
, generated by multiplication operators
and
, haveirreducible representations exactly of dimensions n
0,n
1,..., n
m
.This work was partially supported by CONACYT Project 3114P-E9607, México. 相似文献
2.
It is known [KRS] that for each finitely generated Banach algebra
there exists a numberN such that for eachn>N the matrix algebras
can be generated by three idempotents. In this paper we show that the same statement is true for direct sums
and
, where
is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for
algebras
because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra
can be generated by two idempotents if and only ifn
j
=2 for eachj and
is singly generated. Also we give an example of a free singly generated algebra
for which
can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x%
fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde
{\cal B}}\] can be generated by three idempotents for each singly generated free algebra
. 相似文献
3.
We characterize when positive operators can be factored by analytic Toeplitz type operators. As a corollary, we give an operator theory characterization of those invariant subspaces of doubly commuting unilateral shifts, which are generated by a single inner function on the bidisk. The last result extends to shifts of arbitrary (countable) multiplicity. 相似文献
4.
We analyze the influence of the radial component of a symbol to spectral, compactness, and Fredholm properties of Toeplitz operators, acting on the Bergman space. We show that there existcompact Toeplitz operators whose (radial) symbols areunbounded near the unit circle
. Studying this question we give several sufficient, and necessary conditions, as well as the corresponding examples. The essential spectra of Toeplitz operators with pure radial symbols have sufficiently rich structure, and even can be massive.TheC
*-algebras generated by Toeplitz operators with radial symbols are commutative, but the semicommutators[T
a, Tb)=Ta·Tb–Ta·b are not compact in general. Moreover for bounded operatorsT
a andT
b the operatorT
a·b may not be bounded at all.This work was partially supported by CONACYT Project 27934-E, México.The first author acknowledges the RFFI Grant 98-01-01023, Russia. 相似文献
5.
The structure of theC
*-algebra with identity generated by two orthogonal projections is well understood. All irreducible representations of this algebra are either two-dimensional or one-dimensional. The situation becomes unpredictable in the case of theC
*-algebra generated by three orthogonal projections. Even in the more specific case when two of the projections commute, the algebra under consideration may have infinite dimensional irreducible representations.In this paper we produce three concrete realizations of the algebra generated by three orthogonal projections in that specific case. It turns out that these algebras have quite different structure.This work was partially supported by CONACYT Project 4069-E9404, México. 相似文献
6.
N. L. Vasilevski 《Integral Equations and Operator Theory》1998,31(1):113-132
We study the following problem: Given a Hilbert spaceH and a set of orthogonal projectionsP, Q
1, ..., Qn on it, with the conditionsQ
j
·Q
k
=
j,k
Q
k
,
, describe theC
*-algebraC
*(P, Q
1, ..., Qn) generated by these projections.Applications to Naimark dilation theorems and to Toeplitz operators associated with the Heisenberg group are given.Dedicated to the memory of M. G. Krein.This work was partially supported by CONACYT Project 3114P-E9608, México. 相似文献
7.
In this paper we describe some classes of linear operatorsTL(H) (mainly Toeplitz, Wiener-Hopf and singular integral) on a Hilbert spacesH such that the spectrum (T, L(H)) is continuous at the pointsT from these classes. We also describe some subalgebras
of the algebras for which the spectrum (x,) becomes continuous at the pointsx when (x,) is restricted to the subalgebra
. In particular, we show that the spectrum (x,) is continuous in Banach algebras with polynomial identities. Examples of such algebras are given.This research was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities. 相似文献
8.
Jordan derivations of triangular algebras 总被引:3,自引:0,他引:3
In this note, it is shown that every Jordan derivation of triangular algebras is a derivation. 相似文献
9.
All-derivable points of operator algebras 总被引:1,自引:0,他引:1
Jun Zhu 《Linear algebra and its applications》2007,427(1):1-5
Let A be an operator subalgebra in B(H), where H is a Hilbert space. We say that an element Z∈A is an all-derivable point of A for the norm-topology (strongly operator topology, etc.) if, every norm-topology (strongly operator topology, etc.) continuous derivable linear mapping φ at Z (i.e. φ(ST)=φ(S)T+Sφ(T) for any S,T∈A with ST=Z) is a derivation. In this paper, we show that every invertible operator in the nest algebra is an all-derivable point of the nest algebra for the strongly operator topology. We also prove that every nonzero element of the algebra of all 2×2 upper triangular matrixes is an all-derivable point of the algebra. 相似文献
10.
Jordan higher derivations on triangular algebras 总被引:1,自引:0,他引:1
Zhankui Xiao 《Linear algebra and its applications》2010,432(10):2615-1054
In this paper, we show that any Jordan higher derivation on a triangular algebra is a higher derivation. This extends the main result in [13] to the case of higher derivations. 相似文献
11.
The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators. We obtain a distance formula to an arbitrary WOT-closed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is used to obtain Nevanlinna-Pick type interpolation theoremsFirst author partially supported by an NSERC grant and a Killam Research Fellowship.Second author partially supported by an NSF grant. 相似文献
12.
In this paper, it is shown that every norm continuous linear local derivation from an arbitrary CSL algebra whose lattice is generated by finitely many independent nests into any ultraweakly closed subalgebra which contains the algebra is an inner derivation, and that every norm continuous linear local derivation from an arbitrary CSL algebra whose lattice is completely distributive into any ultraweakly closed subalgebra which contains the algebra is a derivation. 相似文献
13.
In the present note we show asynchronous exponential growth for important age- and size-structured population models. 相似文献
14.
Gerard J. Murphy 《Integral Equations and Operator Theory》1997,27(2):221-227
The class of Toeplitz algebras associated to ordered groups is important in the analysis of Toeplitz operators on the generalised Hardy spaces defined by such groups. The conditions under which these Toeplitz algebras are Type I C*-algebras are investigated. 相似文献
15.
Xiaojun Zheng 《Integral Equations and Operator Theory》1996,24(4):484-496
In this paper we will prove that any unital isometric representation ofH
() with finitely connected domain has property (A
1(r)) for somer1, which generalizes the same conclusion in [2] and [8]. 相似文献
16.
We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach
algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras,
both the left and right topological stable ranks are infinite. We extend this latter result to Popescu’s non-commutative disc
algebras and to free semigroup algebras as well.
K. R. Davidson, L. W. Marcoux, H. Radjavi’s research was supported in part by NSERC (Canada).
An erratum to this article can be found at 相似文献
17.
Xiaofei Qi 《Linear algebra and its applications》2010,432(12):3183-1146
Let N be a nest on a complex Banach space X with N∈N complemented in X whenever N-=N, and let AlgN be the associated nest algebra. We say that an operator Z∈AlgN is an all-derivable point of AlgN if every linear map δ from AlgN into itself derivable at Z (i.e. δ(A)B+Aδ(B)=δ(Z) for any A,B∈A with AB=Z) is a derivation. In this paper, it is shown that if Z∈AlgN is an injective operator or an operator with dense range, or an idempotent operator with ran(Z)∈N, then Z is an all-derivable point of AlgN. Particularly, if N is a nest on a complex Hilbert space, then every idempotent operator with range in N, every injective operator as well as every operator with dense range in AlgN is an all-derivable point of the nest algebra AlgN. 相似文献
18.
19.
A. N. Karapetyants V. S. Rabinovich N. L. Vasilevski 《Integral Equations and Operator Theory》2001,40(3):278-308
We describe the Fredholm symbol algebra for theC
*-algebra generated by two dimensional singular integral operators, acting onL
2(2), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin.These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.Rostov State University RussiaPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-EPartially supported by CONACYT Project 27934-E, México. 相似文献
20.
Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras 总被引:1,自引:0,他引:1
A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(T−S))=w(T−S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let and be two atomic nests on complex Hilbert spaces H and K, respectively. Denote the nest algebra associated with and the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometries from onto and a thorough classification of numerical radius isometries from onto . 相似文献