共查询到20条相似文献,搜索用时 15 毫秒
1.
Don Hadwin 《Mathematische Annalen》2000,316(2):201-213
We show that if S is a pure subnormal operator, then the minimal normal extension can be written as with . We also extend the Kaplansky density theorem by proving that if is a unital -algebra of operators, then every subnormal contraction in is a (SOT) limit of normal contractions in . We prove similar results for subnormal tuples.
Received: 26 July 1998 / in final form: 30 March 1999 相似文献
2.
Daoxing Xia 《Integral Equations and Operator Theory》1993,17(3):417-439
Trace formulas are established for the product of commutators related to subnormal tuple of operators (S
1,...,S
n
) with minimal normal extension (N
1,...,N
n
) satisfying conditions that sp(S
j
)/sp(N
j
) is simply-connected with smooth boundary Jordan curve sp(N
i
) and [S
j
*
,S
j
]1/2 L
1,j=1, 2,...,n.Some complete unitary invariants related to the trace formulas are found.This work is supported in part by NSF Grant no. DMS-9101268. 相似文献
3.
Jasang Yoon 《Journal of Mathematical Analysis and Applications》2007,333(2):626-641
In this paper we study the hyponormality and subnormality of 2-variable weighted shifts using the Schur product techniques in matrices. As applications, we generalize the result in [R. Curto, J. Yoon, Jointly hyponormal pairs of subnormal operators need not be jointly subnormal, Trans. Amer. Math. Soc. 358 (2006) 5135-5159, Theorem 5.2] and give a non-trivial, large class satisfying the Curto-Muhly-Xia conjecture [R. Curto, P. Muhly, J. Xia, Hyponormal pairs of commuting operators, Oper. Theory Adv. Appl. 35 (1988) 1-22] for 2-variable weighted shifts. Further, we give a complete characterization of hyponormality and subnormality in the class of flat, contractive, 2-variable weighted shifts T≡(T1,T2) with the condition that the norm of the 0th horizontal 1-variable weighted shift of T is a given constant. 相似文献
4.
In this paper, we use the mosaic of a subnormal operator given by Daoxing Xia to give an alternate definition of the Pincus
principal function for pure subnormal operators. This allows us to provide much simplified proofs of some of the basic properties
of the principal function and of the Carey-Helton-Howe-Pincus Theorem in the subnormal case. 相似文献
5.
《Journal of Differential Equations》1987,66(2):151-164
In this paper we give some geometric criteria (analogous to Wiener's, Poincaré's and Zaremba's criteria for the Laplacian) for the regularity of boundary points for the Dirichlet problem relative to a class of partial differtial operators of the form ∑j = 1n Xj2, fulfilling Hörmander's condition. 相似文献
6.
We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators Aj on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators. 相似文献
7.
In this paper it is shown that if T∈L(H) satisfies
- (i)
- T is a pure hyponormal operator;
- (ii)
- [T∗,T] is of rank two; and
- (iii)
- ker[T∗,T] is invariant for T,
8.
We discuss here representation and Fredholm theory for C1-algebras generated by commuting isometries. More particularly, for n commuting isometries {Vj: 1 ? j ? n} on separable Hilbert space we give a representation resembling the well-known representation for a single isometry. Our representation permits an analysis of the C1-algebras =(Vj:1?j?n) generated by the {Vj}. The commutator ideal in is identified precisely and, under certain additional hypotheses, the Fredholm operators in are also precisely determined. Finally, we obtain formulas in terms of topological data for the index of Fredholm operators in some interesting algebras of the type (Vj:1?j?n). 相似文献
9.
In this paper, we introduce Xia spectra of n-tuples of operators satisfying |T
2| ≥ U|T
2|U* for the polar decomposition of T = U|T| and we extend Putnam’s inequality to these tuples [7].
This research is partially supported by Grant-in-Aid Research No.17540176. 相似文献
10.
Mellin's transform is used to establish a functional calculus of a class of pseudodifferential-operators depending on a small parameter h > 0. We apply for exeample this result to prove the semi-classical behaviour of the discrete spectrum of Schrödinger operators ?h2 · Δ + V, and of Dirac operators h ∑j = 13αjDj + α4 ? V. 相似文献
11.
We consider tuples {N jk }, j = 1, 2, ..., k = 1, ..., q j , of nonnegative integers such that $$ \sum\limits_{j = 1}^\infty {\sum\limits_{k = 1}^{q_j } {jN_{jk} } } \leqslant M. $$ Assuming that q j ~ j d?1, 1 < d < 2, we study how the probabilities of deviations of the sums $ \sum\nolimits_{j = j_1 }^{j_2 } {\sum\nolimits_{k = 1}^{q_j } {N_{jk} } } $ N jk from the corresponding integrals of the Bose-Einstein distribution depend on the choice of the interval [j 1,j 2]. 相似文献
12.
O. I. Mokhov 《Theoretical and Mathematical Physics》2011,167(1):403-420
We study bi-Hamiltonian systems of hydrodynamic type with nonsingular (semisimple) nonlocal bi-Hamiltonian structures. We
prove that all such systems of hydrodynamic type are diagonalizable and that the metrics of the bi-Hamiltonian structure completely
determine the complete set of Riemann invariants constructed for any such system. Moreover, we prove that for an arbitrary
nonsingular (semisimple) nonlocally bi-Hamiltonian system of hydrodynamic type, there exist local coordinates (Riemann invariants)
such that all matrix differential-geometric objects related to this system, namely, the matrix (affinor) Vji(u) of this system of hydrodynamic type, the metrics g
1
ij(u) and g
2
ij(u), the affinor υji(u) = g
1
is(u)g
2,sj(u), and also the affinors (w
1,n)ji(u) and (w
2,n)ji(u) of the nonsingular nonlocal bi-Hamiltonian structure of this system, are diagonal in these special “diagonalizing” local
coordinates (Riemann invariants of the system). The proof is a natural corollary of the general results of our previously
developed theories of compatible metrics and of nonlocal bi-Hamiltonian structures; we briefly review the necessary notions
and results in those two theories. 相似文献
13.
By solving a free analog of the Monge-Ampère equation, we prove a non-commutative analog of Brenier’s monotone transport theorem: if an n-tuple of self-adjoint non-commutative random variables Z 1,…,Z n satisfies a regularity condition (its conjugate variables ξ 1,…,ξ n should be analytic in Z 1,…,Z n and ξ j should be close to Z j in a certain analytic norm), then there exist invertible non-commutative functions F j of an n-tuple of semicircular variables S 1,…,S n , so that Z j =F j (S 1,…,S n ). Moreover, F j can be chosen to be monotone, in the sense that and g is a non-commutative function with a positive definite Hessian. In particular, we can deduce that C ?(Z 1,…,Z n )?C ?(S 1,…,S n ) and \(W^{*}(Z_{1},\dots,Z_{n})\cong L(\mathbb{F}(n))\) . Thus our condition is a useful way to recognize when an n-tuple of operators generate a free group factor. We obtain as a consequence that the q-deformed free group factors \(\varGamma_{q}(\mathbb{R}^{n})\) are isomorphic (for sufficiently small q, with bound depending on n) to free group factors. We also partially prove a conjecture of Voiculescu by showing that free Gibbs states which are small perturbations of a semicircle law generate free group factors. Lastly, we show that entrywise monotone transport maps for certain Gibbs measure on matrices are well-approximated by the matricial transport maps given by free monotone transport. 相似文献
14.
Chandler Davis 《Linear algebra and its applications》1977,18(1):33-43
Problem: Given operators Aj ? O on Hilbert space , with ΣAj = 1, to find commuting projectors Ej on a Hilbert space ? such that (for all j) x1Ajy = x1Ejy for, x, y ∈ . This paper gives an explicit construction, quite different from the familiar solution. 相似文献
15.
An n-frame on a Banach space is E=(E1,?, En) where the Ej's are bounded linear operators on such that Ej≠0, , and EjEk=δjkEk (j, k=1,?, n). It is known that if two n-frames E and F are sufficiently close to each other, then they are similar, that is, Fj=TEjT-1 with T a bounded linear operator. Among the operators which realize the similarity of the two frames, there is the balanced transformation U(F, E)=(Σnj=1FjEj)(Σnj=1EjFjEj). One of our main results is a local characterization of the balanced transformation. Another operator which implements the similarity between E and F is the direct rotation R(F, E). It comes up in connection with the study of the set of all n-frames as a Banach manifold with an affine connection. Finally, it is shown that for quite a large set of pairs of 2-frames, the direct rotation has a global characterization. 相似文献
16.
Jean-Christophe Aval 《Discrete Mathematics》2002,256(3):557-575
The aim of this work is to study some lattice diagram determinants ΔL(X,Y) as defined in (Adv. Math. 142 (1999) 244) and to extend results of Aval et al. (J. Combin. Theory Ser. A, to appear). We recall that ML denotes the space of all partial derivatives of ΔL. In this paper, we want to study the space Mi,jk(X,Y) which is defined as the sum of ML spaces where the lattice diagrams L are obtained by removing k cells from a given partition, these cells being in the “shadow” of a given cell (i,j) in a fixed Ferrers diagram. We obtain an upper bound for the dimension of the resulting space Mi,jk(X,Y), that we conjecture to be optimal. This dimension is a multiple of n! and thus we obtain a generalization of the n! conjecture. Moreover, these upper bounds associated to nice properties of some special symmetric differential operators (the “shift” operators) allow us to construct explicit bases in the case of one set of variables, i.e. for the subspace Mi,jk(X) consisting of elements of 0 Y-degree. 相似文献
17.
Mao-Ting Chien Hiroshi Nakazato 《Journal of Mathematical Analysis and Applications》2011,373(1):297-304
Let r be a real number and A a tridiagonal operator defined by Aej=ej−1+rjej+1, j=1,2,…, where {e1,e2,…} is the standard orthonormal basis for ?2(N). Such tridiagonal operators arise in Rogers-Ramanujan identities. In this paper, we study the numerical ranges of these tridiagonal operators and finite-dimensional tridiagonal matrices. In particular, when r=−1, the numerical range of the finite-dimensional tridiagonal matrix is the convex hull of two explicit ellipses. Applying the result, we obtain that the numerical range of the tridiagonal operator is the square
18.
Zoltán Finta 《Central European Journal of Mathematics》2013,11(12):2257-2261
For certain generalized Bernstein operators {L n } we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e i (x) = x i and e j (x) = x j are preserved by L n for each n = 1, 2,… But there exist infinitely many e i such that e 0(x) = 1 and e j (x) = x j are its fixed points. 相似文献
19.
Schrödinger operators with infinite-rank singular potentials V=Σ i,j=1 ∞ b ij〈φj,·〉φi are studied under the condition that the singular elements ψ j are ξ j(t)-invariant with respect to scaling transformationsin ?3. 相似文献
20.
Allen Devinatz 《Journal of Functional Analysis》1979,32(3):312-335
Let Ω be a domain in Rn and T = ∑j,k = 1n(?j ? ibj(x)) ajk(x)(?k ? ibk(x)), where the ajk and the bj are real valued functions in , and the matrix (ajk(x)) is symmetric and positive definite for every . If T0 is the same as T but with bj = 0, j = 1,…, n, and if u and Tu are in , then T. Kato has established the distributional inequality ū) Tu]. He then used this result to obtain selfadjointness results for perturbed operators of the form T ? q on Rn. In this paper we shall obtain Kato's inequality for degenerate-elliptic operators with real coefficients. We then use this to get selfadjointness results for second order degenerate-elliptic operators on Rn. 相似文献