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1.
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
2.
On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols
have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products
with four factors. We also prove a local version of this result for products with three factors. 相似文献
3.
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
4.
Let D be a bounded logarithmically convex complete Reinhardt domain in
centered at the origin. Generalizing a result for the one-dimensional case of the unit disk, we prove that the C
*-algebra generated by Toeplitz operators with bounded measurable separately radial symbols (i.e., symbols depending only on
is commutative.
We show that the natural action of the n-dimensional torus
defines (on a certain open full measure subset of D) a foliation which carries a transverse Riemannian structure having distinguished geometric features. Its leaves are equidistant
with respect to the Bergman metric, and the orthogonal complement to the tangent bundle of such leaves is integrable to a
totally geodesic foliation. Furthermore, these two foliations are proved to be Lagrangian.
We specify then the obtained results for the unit ball. 相似文献
5.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
6.
We introduce the concept of Lp-maximal regularity for second order Cauchy problems. We prove Lp-maximal regularity for an abstract model problem and we apply the abstract results to prove existence, uniqueness and regularity
of solutions for nonlinear wave equations.
The author acknowledges with thanks the support provided by the Department ofApplied Analysis, University of Ulm, and the
travel grants provided by NBMH India and MSF Delhi, India. 相似文献
7.
Let B(H) denote the algebra of operators on a complex separable
Hilbert space H, and let A $\in$ B(H) have the polar decomposition A = U|A|.
The Aluthge transform
is defined to be the operator
.
We say that A $\in$ B(H) is p-hyponormal,
.
Let
.
Given p-hyponormal
, such that AB is compact, this
note considers the relationship between
denotes an enumeration in decreasing order repeated according
to multiplicity of the eigenvalues of the
compact operator T (respectively,
singular values of the compact operator T).
It is proved that
is bounded above by
and below by
for all j = 1, 2, . . .
and that if also
is normal, then there exists a unitary
U1 such that
for all j = 1, 2, . . .. 相似文献
8.
Michael T. Jury 《Integral Equations and Operator Theory》2007,58(3):341-362
We analyze the essential sectrum and index theory of elements of Toeplitz-composition C*-algebras (algebras generated by the Toeplitz algebra and a single linear-fractional composition operator, acting on the Hardy
space of the unit disk). For automorphic composition operators we show that the quotient of the Toeplitz-composition algebra
by the compacts is isomorphic to the crossed product C*-algebra for the action of the symbol on the boundary circle. Using this result we obtain sufficient conditions for polynomial
elements of the algebra to be Fredholm, by analyzing the spectrum of elements of the crossed product. We also obtain an integral
formula for the Fredholm index in terms of a generalized Chern character. Finally we prove an index formula for the case of
the non-parabolic, non-automorphic linear fractional maps studied by Kriete, MacCluer and Moorhouse. 相似文献
9.
Raul Quiroga-Barranco A. Sanchez-Nungaray 《Integral Equations and Operator Theory》2011,71(2):225-243
We prove the existence of commutative C*-algebras of Toeplitz operators on every weighted Bergman space over the complex projective space
\mathbbPn\mathbb(C){{\mathbb{P}^n}\mathbb{(C)}}. The symbols that define our algebras are those that depend only on the radial part of the homogeneous coordinates. The algebras
presented have an associated pair of Lagrangian foliations with distinguished geometric properties and are closely related
to the geometry of
\mathbbPn\mathbb(C){{\mathbb{P}^n}\mathbb{(C)}}. 相似文献
10.
In this note we examine the relationships between p-hyponormal
operators and the operator inequality
. This leads to a method for
generating examples of p-hyponormal operators which are not q-hyponormal
for any
. Our methods are also shown to have implications for the class
of Furuta type inequalities. 相似文献
11.
José E. Galé Pedro J. Miana Detlef Müller 《Integral Equations and Operator Theory》2007,57(3):327-337
We consider some extensions of well-boundedness and Cm-scalarity by using fractional calculus, and prove some theorems accordingly. These results are applied to the usual Laplacian
on Rn and sub-Laplacians on nilpotent Lie groups.
The research of first and second authors has been partly supported by the Project MTM2004-03036 of the M.C.YT.-DGI/F.E.D.E.R.,
Spain, and the Project E-12/25, D. G. Aragón, Spain. Part of the research of second author was developed in the Christian-Albrechts
Universit?t in Kiel, while he was enjoying a HARP-postdoctoral position in the European Harmonic Analysis Network, HARP, IHP
2002-06. 相似文献
12.
Given
, a compact abelian group G and a function
, we identify the maximal (i.e. optimal) domain of the convolution
operator
(as an operator from Lp(G) to itself). This is the
largest Banach function space (with order continuous norm) into which Lp(G)
is embedded and to which
has a continuous extension, still with values
in Lp(G). Of course, the optimal domain depends on p and g. Whereas
is compact, this is not always so for the extension of
to its optimal domain.
Several characterizations of precisely when this is the case are presented. 相似文献
13.
Products of Toeplitz Operators on the Bergman Space 总被引:1,自引:0,他引:1
Issam Louhichi Elizabeth Strouse Lova Zakariasy 《Integral Equations and Operator Theory》2006,54(4):525-539
In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a
Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic
symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions
for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases
(Theorem 6.4), and then show that almost anything can happen (Theorem 6.7). 相似文献
14.
Let be a positive C
0-semigroup on L
p
(Ω), with infinitesimal
generator A. In this paper, it is proved that if there exists a such that and ,
where A
*
is the adjoint of A, then the growth bound of T(t) is upper bounded
by b when p = 1, and by when 1 lt; p lt; α and c D(A), where .
This is an operator version of a classical stability result
on Z-matrix. As application examples, some new results on the asymptotic
behaviours of population system and neutron transport system are obtained.
Submitted: March 1, 2001?Revised: August 28, 2002 相似文献
15.
We show that, if a simple C*-algebra A is topologically finite-dimensional in a suitable sense, then not only K0(A) has certain good properties, but A is even accessible to Elliott’s classification program. More precisely, we prove the following results:If A is simple, separable and unital with finite decomposition rank and real rank zero, then K0(A) is weakly unperforated.If A has finite decomposition rank, real rank zero and the space of extremal tracial states is compact and zero-dimensional, then A has stable rank one and tracial rank zero. As a consequence, if B is another such algebra, and if A and B have isomorphic Elliott invariants and satisfy the Universal coefficients theorem, then they are isomorphic.In the case where A has finite decomposition rank and the space of extremal tracial states is compact and zero-dimensional, we also give a criterion (in terms of the ordered K0-group) for A to have real rank zero. As a byproduct, we show that there are examples of simple, stably finite and quasidiagonal C*-algebras with infinite decomposition rank.Supported by: EU-Network Quantum Spaces - Noncommutative Geometry (Contract No. HPRN-CT-2002-00280) and Deutsche Forschungsgemeinschaft (SFB 478). 相似文献
16.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
17.
Inspired by the problem of powers of hyponormal operators, this paper is to discuss the structure on powers of p-hyponormal and log-hyponormal operators. The structure on powers of operators consists of same-side structure and different-side
structure. The same-side structure means relations between and , and the different-side structure means relations between where m, n are positive integers and T is a bounded linear operator on a Hilbert space. Thus, the original problem of powers of hyponormal operators belongs to
different-side structure on powers of hyponormal operators. The structure on powers of p-hyponormal operators for p > 0 is emphasized. Also, some applications are obtained.
相似文献
18.
In this paper it is shown that the normal parts of quasisimilar
p-hyponormal operators are unitarily equivalent, a p-hyponormal operator
compactly quasisimilar to an isometry is normal, and a p-hyponormal spectral
operator is normal. 相似文献
19.
Chun-Gil Park Hahng-Yun Chu Won-Gil Park Hee-Jeong Wee 《Czechoslovak Mathematical Journal》2005,55(4):1055-1065
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra
into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all unitaries u ∈
, all y ∈
, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra
of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all u ∈ {v ∈
: v = v* and v is invertible}, all y ∈
and all n ∈ ℤ.
Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.
This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008.
The second author was supported by the Brain Korea 21 Project in 2005. 相似文献
20.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献