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1.
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
2.
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space
, the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with
respect to fixed orthonormal bases) are functions having real Fourier coefficients, or equivalently, each matrix entry f satisfies
for all z ∈
.
Tolokonnikov’s Lemma for
means that if f is left-invertible, then f can be completed to an isomorphism; that is, there exists an F, invertible in
, such that F = [ f f
c
] for some f
c
in
. In control theory, Tolokonnikov’s Lemma implies that if a function has a right coprime factorization over
, then it has a doubly coprime factorization in
. We prove the lemma for the real disc algebra
as well. In particular,
and
are Hermite rings.
The work of the first author was supported by Magnus Ehrnrooth Foundation.
Received: December 5, 2006. Revised: February 4, 2007. 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.
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
5.
Onur Yavuz 《Integral Equations and Operator Theory》2007,58(3):433-446
We consider a multiply connected domain
where
denotes the unit disk and
denotes the closed disk centered at
with radius r
j
for j = 1, . . . , n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded, then there exists a nontrivial common invariant subspace for T
* and (T − λ
j
I)*-1. 相似文献
6.
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
7.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
8.
Muneo Chō Mariko Giga Tadasi Huruya Takeaki Yamazaki 《Integral Equations and Operator Theory》2007,57(3):303-308
Let
be an invertible class A operator such that
. Then we show that
, where gT is the principal function of T. Moreover, we show that if T is pure, then
. 相似文献
9.
Kazem Khashyarmanesh 《Archiv der Mathematik》2007,88(5):413-418
Let (
) be a commutative Noetherian local ring with non-zero identity,
an ideal of R and M a finitely generated R-module with
. Let D(–) := Hom
R
(–, E) be the Matlis dual functor, where
is the injective hull of the residue field
. We show that, for a positive integer n, if there exists a regular sequence
and the i-th local cohomology module H
i
a
(M) of M with respect to
is zero for all i with i > n then
The author was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran
(No. 85130023).
Received: 9 August 2006 相似文献
10.
Let G be a connected simply connected almost
-simple algebraic group with
non-compact and
a cocompact congruence subgroup. For any homogeneous manifold
of finite volume, and a
, we show that the Hecke orbit T
a
(x
0
H) is equidistributed on
as
, provided H is a non-compact commutative reductive subgroup of G. As a corollary, we generalize the equidistribution result of Hecke points ([COU], [EO1]) to homogeneous spaces G/H. As a concrete application, we describe the equidistribution result in the rational matrices with a given characteristic
polynomial.
The second author partially supported by DMS 0333397.
Received: May 2005 Revision: March 2006 Accepted: June 2006 相似文献
11.
Henrik Petersson 《Integral Equations and Operator Theory》2007,57(3):413-423
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies
, the conjugate operator
is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an
such that
is dense in S(H). We generalize the result to more general conjugate maps
, and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively. 相似文献
12.
Anders Olofsson 《Integral Equations and Operator Theory》2007,58(4):503-549
We study an operator-valued Berezin transform corresponding to certain standard weighted Bergman spaces of square integrable
analytic functions in the unit disc. The study of this operator-valued Berezin transform relates in a natural way to the study
of the class of n-hypercontractions on Hilbert space introduced by Agler. To an n-hypercontraction
we associate a positive
-valued operator measure dω
n, T
supported on the closed unit disc
in a way that generalizes the above notion of operator-valued Berezin transform. This construction of positive operator measures
dω
n, T
gives a natural functional calculus for the class of n-hypercontractions. We revisit also the operator model theory for the class of n-hypercontractions. The new results here concern certain canonical features of the theory. The operator model theory for the
class of n-hypercontractions gives information about the structure of the positive operator measures dω
n, T
. 相似文献
13.
Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β (2n)={ β ij } i,j ≥ 0,i+j ≤ 2n , with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that
We prove that β admits a Q-representing measure μ (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated, has a column relation Q(X,Y) = 0, and the algebraic variety
associated to β satisfies card
In this case,
if
then β admits a rank
-atomic (minimal) Q-representing measure; if
then β admits a Q-representing measure μ satisfying
相似文献
14.
Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrices 总被引:1,自引:0,他引:1
Li Xia YE Zhi Xiang WU Xue Feng MEI 《数学学报(英文版)》2007,23(10):1729-1744
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d(y), which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d(y) and weak A-forms of wUq^d(y). 相似文献
15.
Yong Ge TIAN 《数学学报(英文版)》2006,22(1):289-300
For any element a in a generalized 2^n-dimensional Clifford algebra Lln (F) over an arbitrary field F of characteristic not equal to two, it is shown that there exits a universal invertible matrix Pn over Lln(F) such that Pn^-1DnPn= φ(α)∈F^2n×2n, where φ(a) is a matrix representation of α over and Dα is a diagonal matrix consisting of a or its conjugate. 相似文献
16.
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
17.
J. J. Grobler 《Integral Equations and Operator Theory》2007,57(1):83-99
For a probability space
we denote the marginal measures of
, defined on Σ and Λ respectively, by
and
. If ρ is a function norm defined on
marginal function norms ρ1 and ρ2 are defined on
and
. We find conditions which guarantee Lρ 1 + Lρ 2 to be embedded in Lρ as a closed subspace. The problem is encountered in Statistics when estimating a bivariate distribution with known marginals.
We find a condition which, applied to the binormal distribution in L2, improves some known conditions. 相似文献
18.
Here we study complete rotation hypersurfaces with constant k-th mean curvature Hk in
even and 2 < k < n. We prove the existence of a constant
such that there are no such hypersurfaces for
. We have only one compact hypersurface of this kind with
. For each
there is a corresponding family of complete immersed rotation hypersurfaces, each family containing two isoparametric hypersurfaces.
For Hk ≥ 0, there is also such a family, now containing only one isoparametric hypersurface. Finally, we prove the existence of
compact hypersurfaces with arbitrarily large Hk , neither isometric to a sphere nor to a product of spheres.
*Bull. Braz. Math. Soc. 30 (2), 1999, 139–161.
**Partially supported by FUNCAP, Brazil.
***Partially supported by CNPq, Brazil and DGAPA-UNAM, México. 相似文献
19.
Let
be the 2k-uniform hypergraph obtained by letting P1, . . .,Pr be pairwise disjoint sets of size k and taking as edges all sets Pi∪Pj with i ≠ j. This can be thought of as the ‘k-expansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain
can be obtained by partitioning V = V1 ∪V2 and taking as edges all sets of size 2k that intersect each of V1 and V2 in an odd number of elements. Let
denote a hypergraph on n vertices obtained by this construction that has as many edges as possible. For n sufficiently large we prove a conjecture of Frankl, which states that any hypergraph on n vertices that contains no
has at most as many edges as
.
Sidorenko has given an upper bound of
for the Tur′an density of
for any r, and a construction establishing a matching lower bound when r is of the form 2p+1. In this paper we also show that when r=2p+1, any
-free hypergraph of density
looks approximately like Sidorenko’s construction. On the other hand, when r is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Turán density
of
to
, where c(r) is a constant depending only on r.
The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections
in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear
algebra, the Kruskal–Katona theorem and properties of Krawtchouck polynomials.
* Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship. 相似文献
20.
Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo 《Complex Analysis and Operator Theory》2007,1(2):211-233
Passive linear systems τ =
have their transfer function
in the Schur class S
. Using a parametrization of contractive block operators the transfer function
is connected to the Sz.-Nagy–Foiaş characteristic function
of the contraction A. This gives a new aspect and some explicit formulas for studying the interplay between the system τ and the functions
and
. The method leads to some new results for linear passive discrete-time systems. Also new proofs for some known facts in
the theory of these systems are obtained.
Dedicated to Eduard Tsekanovskiĭ on the occasion of his seventieth birthday
This work was supported by the Research Institute for Technology at the University of Vaasa.
The first author was also supported by the Academy of Finland (projects 212146, 117617) and the Dutch Organization for Scientific
Research N.W.O. (B 61-553).
Received: December 22, 2006. Revised: February 6, 2007. 相似文献