共查询到20条相似文献,搜索用时 31 毫秒
1.
We give a new proof of the operator version of the Fejér-Riesz
Theorem using only ideas from elementary operator theory. As an outcome,
an algorithm for computing the outer polynomials that appear in the Fejér-Riesz
factorization is obtained. The extremal case, where the outer factorization
is also *-outer, is examined in greater detail. The connection to Aglers
model theory for families of operators is considered, and a set of families lying
between the numerical radius contractions and ordinary contractions is
introduced. The methods are also applied to the factorization of multivariate
operator-valued trigonometric polynomials, where it is shown that the factorable
polynomials are dense, and in particular, strictly positive polynomials
are factorable. These results are used to give results about factorization of
operator valued polynomials over
, in terms of rational functions
with fixed denominators. 相似文献
2.
Bojan Mohar 《Linear algebra and its applications》2010,432(9):2273-2467
Wilf’s eigenvalue upper bound on the chromatic number is extended to the setting of digraphs. The proof uses a generalization of Brooks’ Theorem to digraph colorings. 相似文献
3.
Motivated with a problem in spectroscopy, Sloane and Harwit conjectured in 1976 what is the minimal Frobenius norm of the inverse of a matrix having all entries from the interval [0,1]. In 1987, Cheng proved their conjecture in the case of odd dimensions, while for even dimensions he obtained a slightly weaker lower bound for the norm. His proof is based on the Kiefer–Wolfowitz equivalence theorem from the approximate theory of optimal design. In this note we give a short and simple proof of his result. 相似文献
4.
Adam Kleppner 《Integral Equations and Operator Theory》1996,25(4):490-495
We give a short proof of the Cyclic Decomposition Theorem. The proof proceeds by induction on the dimension of the space in the case that the minimal polynomial of the operator has only one irreducible factor and then uses the Primary Decomposition Theorem to treat the general case. 相似文献
5.
In this note we present a new proof and an extension of the Hilbert space operators version of an inequality by Bohr. 相似文献
6.
The general representation for the elements of the inverse of any Hessenberg matrix of finite order is here extended to the reduced case with a new proof. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences of unbounded order for such computations on matrices of intermediate order, and some elementary properties of the inverse. These results are applied on the resolvent matrix associated to a finite Hessenberg matrix in standard form. Two examples on the unit disk are given. 相似文献
7.
We continue the study of a generalization of L. de Branges's theory of Hilbert spaces of entire functions to the Pontryagin space setting. In this-second-part we investigate isometric embeddings of spaces of entire functions into spacesL
2 () understood in a distributional sense and consider Weyl coefficients of matrix chains. The main task is to give a proof of an indefinite version of the inverse spectral theorem for Nevanlinna functions. Our methods use the theory developed by L. de Branges and the theory of extensions of symmetric operators of M.G.Krein. 相似文献
8.
S.W. Drury 《Linear algebra and its applications》2008,428(1):305-315
Let T1,…,Td be linear contractions on a complex Hilbert space and p a complex polynomial in d variables which is a sum of d single variable polynomials. We show that the operator norm of p(T1,…,Td) is bounded by
9.
Let Cp be the Schatten p-class for p>0. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: if A={A1,A2,…,An} and B={B1,B2,…,Bn} are two sets of operators in, then C2
10.
Michael Didas 《Integral Equations and Operator Theory》2005,52(4):599-604
Let H be a separable complex Hilbert space. A commuting tuple
of bounded linear operators on H is called a spherical isometry if the relation
holds. In this note it is shown that each spherical isometry is reflexive. 相似文献
11.
In this paper, by applying jointly concavity and jointly convexity of generalized perspective of some elementary functions, we give the simplest proof of the well-known Lieb concavity theorem and Ando convexity theorem. 相似文献
12.
Pei Yuan Wu 《Integral Equations and Operator Theory》2006,56(4):559-569
Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C0(N) contraction if and only if
, where U is a singular unitary operator with multiplicity
and x1, . . . , xd are orthonormal vectors satisfying
. For a C0(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors. 相似文献
13.
Mitsuru Uchiyama 《Integral Equations and Operator Theory》2000,37(1):95-105
LetA, B be bounded selfadjoint operators on a Hilbert space. We will give a formula to get the maximum subspace
such that
is invariant forA andB, and
. We will use this to show strong monotonicity or strong convexity of operator functions. We will see that when 0≤A≤B, andB−A is of finite rank,A
t
≤B
t
for somet>1 if and only if the null space ofB−A is invariant forA. 相似文献
14.
We prove that if the indicator-function1
E
of a measurable setE is a Fourier multiplier in the spaceE
p
() for somep2 thenE is an open set (up to a set of measure zero). 相似文献
15.
Giovanni Vidossich 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):618-623
This paper provides a generalization of the main lemma and a correct proof of an extended version of Theorem 2, in [G. Vidossich, Differential inequalities for evolution equations, Nonlinear Anal. TMA 25 (1995) 1063-1069]. 相似文献
16.
We give a simple and entirely elementary proof of Gasper's Theorem on the Markov sequence problem for Jacobi polynomials. It is based on the spectral analysis of an operator that arises in the study of a probabilistic model of colliding molecules introduced by Marc Kac, and the methods developed here yield new estimates relevant to the collision model. 相似文献
17.
A functional analytic proof of the existence of Krein's spectral shift function and the associated trace formula is given for a pair of unitary operators, the difference of which is trace class.The first author acknowledges with thanks financial support from the Department of Atomic Energy, India through N.B.H.M. of a Post Doctoral Fellowship.The second author thanks the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore for support. 相似文献
18.
For an operator-valued function in the Schur class a new geometric proof, using state space considerations only, of the construction of a minimal and optimal realization is given. A minimal and optimal realization also appears as a restricted shift realization where the state space is the completion of the range of the associated Hankel operator in the de Branges-Rovnyak norm associated with . It is also shown that minimal and optimal, and minimal and star-optimal realizations of a rational matrix function in the Schur class are intimately connected to the extremal positive solutions of the associated Kalman-Yakubobich-Popov operator inequality.The first author thanks the International Association for the promotion of co-operation with scientists from the New Independent States of the former Soviet Union for its support (under project INTAS 93-249), and the Vrije Universiteit, Amsterdam, for its hospitality 相似文献
19.
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given. 相似文献
20.
M. Bekker 《Integral Equations and Operator Theory》1999,35(4):379-397
The extension problem for positive definite Generalized Toeplitz Kernels defined on a finite interval of the real axis is discussed. This problems contains the Krein's extension problem for a positive definite function as a particular case. Criteria of uniqueness of extension is obtained. All extension are described in a complitely indeterminate case. 相似文献