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1.
We study the problem of determining which bounded linear operator on a Hilbert space can be dilated to a singular unitary operator. Some of the partial results we obtained are (1) every strict contraction has a diagonal unitary dilation, (2) every C
0 contraction has a singular unitary dilation, and (3) a contraction with one of its defect indices finite has a singular unitary dilation if and only if it is the direct sum of a singular unitary operator and a C
0( N) contraction. Such results display a scenario which is in marked contrast to that of the classical case where we have the absolute continuity of the minimal unitary power dilation of any completely nonunitary contraction. 相似文献
4.
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided. 相似文献
6.
This article completes a previous investigation of balanced and unitary numerical semigroups. The main result establishes the equivalence of unitary numerical semigroups and perfect 2 × 2 bricks. 相似文献
7.
A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself. A special case of unitary system is a discrete unitary group. We prove that for many (and perhaps all) discrete unitary groups, the set of wandering vector multipliers is itself a group. We completely characterize the wandering vector multipliers for abelian and ICC unitary groups. Some characterizations of special wandering vector multipliers are obtained for other cases. In particular, there are simple characterizations for diagonal and permutation wandering vector multipliers. Similar results remain valid for irrational rotation unitary systems. We also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups. There are applications to wavelet systems. 相似文献
8.
We use methods of the general theory of congruence and *congruence for complex matrices – regularization and cosquares – to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ā A (respectively, A 2) is normal. As special cases of our canonical forms, we obtain – in a coherent and systematic way – known canonical forms for conjugate normal, congruence normal, coninvolutory, involutory, projection, λ-projection, and unitary matrices. But we also obtain canonical forms for matrices whose squares are Hermitian or normal, and other cases that do not seem to have been investigated previously. We show that the classification problems under (a) unitary *congruence when A 3 is normal, and (b) unitary congruence when Aā A is normal, are both unitarily wild, so these classification problems are hopeless. 相似文献
9.
It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional
parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal unitary extensions
of a partially defined isometry constructed explicitly from the problem data. A special role is played by a particular unitary
extension, called the central or universal unitary extension. The coefficient matrix for the Redheffer linear-fractional map has a simple expression in terms of the universal unitary
extension. The universal unitary extension can be seen as a unitary coupling of four unitary operators (two bilateral shift
operators together with two unitary operators coming from the problem data) which has special geometric structure. We use
this special geometric structure to obtain an inverse theorem (Theorem 8.4) which characterizes the coefficient matrices for
a Redheffer linear-fractional map arising in this way from a lifting problem. The main tool is the formalism of unitary scattering
systems developed in Boiko et al. (Operator theory, system theory and related topics (Beer-Sheva/Rehovot 1997), pp. 89–138,
2001) and Kheifets (Interpolation theory, systems theory and related topics, pp. 287–317, 2002) 相似文献
10.
An algorithm for computing the complete CS decomposition of a partitioned unitary matrix is developed. Although the existence
of the CS decomposition (CSD) has been recognized since 1977, prior algorithms compute only a reduced version. This reduced
version, which might be called a 2-by-1 CSD, is equivalent to two simultaneous singular value decompositions. The algorithm
presented in this article computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks
of a unitary matrix partitioned into a 2-by-2 block structure. The algorithm appears to be the only fully specified algorithm
available. The computation occurs in two phases. In the first phase, the unitary matrix is reduced to bidiagonal block form,
as described by Sutton and Edelman. In the second phase, the blocks are simultaneously diagonalized using techniques from
bidiagonal SVD algorithms of Golub, Kahan, Reinsch, and Demmel. The algorithm has a number of desirable numerical features.
相似文献
11.
In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C~n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S~(2n-1) M are great circles. 相似文献
12.
We establish contractions of discrete series representations of SU(1,n) and of unitary irreducible representations of SU(n+1) to the unitary irreducible representations of the (2 n+1)-dimensional Heisenberg group by use of the Berezin calculus on the coadjoint orbits associated to these representations
by the Kirillov-Kostant method of orbits. 相似文献
13.
设AUG(n,Fq2)是Fq2上的n维仿射酉空间,AUn(Fq2)是Fq2上的n次仿射酉群,设M(m,r)是AUn(Fq2)作用下的(m,r)面的轨道.用L(m,r)表示M(m,r)中面的交生成的集合.讨论了各轨道生成的集合之间的包含关系,一个面属于M(m,r)生成的集合的条件,以及L(m,r)是几何格的充要条件. 相似文献
14.
Motivated by topological quantum field theory, we investigate the geometric aspects of unitary 2-representations of finite
groups on 2-Hilbert spaces, and their 2-characters. We show how the basic ideas of geometric quantization are ‘categorified’
in this context: just as representations of groups correspond to equivariant line bundles, 2-representations of groups correspond
to equivariant gerbes. We also show how the 2-character of a 2-representation can be made functorial with respect to morphisms
of 2-representations. Under the geometric correspondence, the 2-character of a 2-representation corresponds to the geometric
character of its associated equivariant gerbe. This enables us to show that the complexified 2-character is a unitarily fully
faithful functor from the complexified Grothendieck category of unitary 2-representations to the category of unitary conjugation
equivariant vector bundles over the group. 相似文献
15.
There are several well-known facts about unitary similarity transformations of complex n-by- n matrices: every matrix of order n = 3 can be brought to tridiagonal form by a unitary similarity transformation; if n ≥ 5, then there exist matrices that cannot be brought to tridiagonal form by a unitary similarity transformation; for any fixed set of positions (pattern) S whose cardinality exceeds n( n ? 1)/2, there exists an n-by- n matrix A such that none of the matrices that are unitarily similar to A can have zeros in all of the positions in S. It is shown that analogous facts are valid if unitary similarity transformations are replaced by unitary congruence ones. 相似文献
16.
给出了广义酉矩阵与广义(斜)Hermite矩阵的概念,研究了它们的性质及其与酉阵、共轭辛阵、Hermite阵、Hamilton及广义逆矩阵之间的联系;取得了许多新的结果;推广了酉矩阵、Hermite阵与斜Hermite阵间的相应结果,特别将正交阵的广义Cayley分解推广到了广义酉矩阵上;将各类酉矩阵、Hermite矩阵及广义逆矩阵统一了起来. 相似文献
17.
An application of the unitary similarity with the discrete Fourier transform to the algebra of diagonal matrices yields the
algebra of circulants. It turns out that if, in this construction, the unitary similarity is replaced by the unitary congruence,
then the class of the so-called Hankel circulants is obtained. The causes and certain effects of this fact are discussed.
Bibliography: 2 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 121–127. 相似文献
18.
We give an explicit classification of the irreducible unitary representations of the simple Lie group SU(2, 2). 相似文献
19.
为了简化大型行(列)酉对称矩阵的QR分解,研究了行(列)酉对称矩阵的性质,获得了一些新的结果,给出了行(列)酉对称矩阵的QR分解的公式和快速算法,它们可极大地减少行(列)酉对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度.同时推广和丰富了邹红星等(2002)的研究内容,拓宽了实际应用领域的范围. 相似文献
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