Adjoints of slant Toeplitz operators

In this paper, we will use the Birkhoff's ergodic theorem to do some finer analysis on the spectral properties of slant Toeplitz operators. For example, we will show that if is an invertibleL function on the unit circle, then almost every point in (A ^* ) is not an eigenvalue ofA ^* . More specifically, we will show that the point spectrum ofA ^* is contained in a circle with positive radius.     

On the decomposition theorem for meromorphic Fredholm resolvents

In this note results of B. Gramsch and W. Kaballo [8] on the decomposition of meromorphic (semi-) Fredholm resolvents are sharpened. A condition on an Orlicz function is given, under which the singular part in this decomposition can be chosen meromorphic inN , the ideal of -nuclear operators. Then the necessity of this condition is studied. Moreover, it is shown that for the rather steep Orlicz functions relevant to this question,N equalsS , the ideal of -approximable operators.Dedicated to Professor Albert Schneider on the occasion of his 60 ^th birthdayresearch supported by a grant from DAAD     

Grid structure of a ballistic function and a computing instrument with linear potentiometers for its generation

Zusammenfassung Die Arbeit befasst sich mit der ballistischen Beziehung zwischen Schrägdistanzs, Lagewinkel und Geschossflugzeitt zum Ziel im Vakuum.Der 1. Teil behandelt die Gewebestruktur dieser Beziehung. Es zeigt sich, dass sie annähernd ein Sechseckgewebe ist. Eine topologische TransformationS(s), (),T(t) wird so gefunden, dass eine Zerlegung in Funktionen einer Variablen in der FormT(t)=S(s)+() die Beziehungt(s,) mit befriedigender Genauigkeit darstellt (der maximale relative Fehler ist weniger als 1%).Im 2. Teil wird auf dieser Grundlage ein Rechengerät zur Darstellung der Funktiont(s, ) konstruiert, das lineare Potentiometer als Schaltelemente benutzt.     

Orthomodular lattices from 3-dimensional quadratic spaces

If E is a vector space over a field K, then any regular symmetric bilinear form on E induces a polarity on the lattice of all subspaces of E. In the particular case where E is 3-dimensional, the set of all subspaces M of E such that both M and are not N-subspaces (which, in most cases, is equivalent to saying that M is nonisotropic), ordered by inclusion and endowed with the restriction of the above polarity, is an orthomodular lattice T(E, ). We show that if K is a proper subfield of K, with K F₂, and E a 3-dimensional K -subspace of E such that the restriction of to E × E is, up to multiplicative constant, a bilinear form on the K -space E , then T(E , ) is isomorphic to an irreducible 3-homogeneous proper subalgebra of T(E, ). Our main result is a structure theorem stating that, when K is not of characteristic 3, the converse is true, i.e., any irreducible 3-homogeneous proper subalgebra of T(E, ) is of this form. As a corollary, we construct infinitely many finite orthomodular lattices which are minimal in the sense that all their proper subalgebras are modular. In fact, this last result was our initial aim in this paper.Received June 4, 2003; accepted in final form May 18, 2004.     

Sur l'' application de réciprocité pour une surface fibrée en coniques définie sur un corps local

For a proper smooth variety X defined over a local field k, unramified class field theory investigates the reciprocity map _X: SK₁(X) ^ab ₁(X) as introduced by S. Saito. We study this map in the case when X is a surface admitting a proper surjection onto a smooth geometrically connected curve C with a smooth conic as generic fibre. Without any assumption on the reduction of C, we prove that _X is injective modulo n for all n invertible in k and its cokernel is the same as that of _C.     

Level surfaces of non-degenerate functions inR n+1

We study level surfaces of non-degenerate functions inR ⁿ⁺¹. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field for level surfaces of a non-degenerate function and give certain characterizations of when is transversal, by the shape operatorS, the transversal connection , and consider the difference between and the affine normal.     

A note on operator norm inequalities

If P is a positive operator on a Hilbert space H whose range is dense, then a theorem of Foias, Ong, and Rosenthal says that: [(P)]^–1T[(P)]<-12 max {T, P^–1TP} for any bounded operator T on H, where is a continuous, concave, nonnegative, nondecreasing function on [0, P]. This inequality is extended to the class of normal operators with dense range to obtain the inequality [(N)]^–1T[(N)]<-12c² max {tT, N^–1TN} where is a complex valued function in a class of functions called vase-like, and c is a constant which is associated with by the definition of vase-like. As a corollary, it is shown that the reflexive lattice of operator ranges generated by the range NH of a normal operator N consists of the ranges of all operators of the form (N), where is vase-like. Similar results are obtained for scalar-type spectral operators on a Hilbert space.This author gratefully acknowledges the support of Central Michigan University in the form of a Research Professorship.     

Interpolation theorems for a family of spanning subgraphs

Let G be a graph with order p, size q and component number . For each i between p – and q, let be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H is an adjacent edge transformation (AET) implies |(H)-(H^')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M _j() and m _j() be the invariants defined by . It is proved that both M _p–() and m _p–(;) interpolate over , if is continuous with respect to AET, and that M _j() and m _j() interpolate over , if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized.     

Analysis of a class of fractional programming problems

We propose a solution strategy for fractional programming problems of the form max _xx g(x)/ (u(x)), where the function satisfies certain convexity conditions. It is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max _xx g(x) + u(x), where is an exogenous parameter. The proposed strategy combines fractional programming andc-programming techniques. A maximal mean-standard deviation ratio problem is solved to illustrate the strategy in action.     

Geometry and the Jones projection of a state

LetA be a von Neumann algebra and a faithful normal state. ThenO = { ºAd(g ¹) :g G _A }andU = { ºAd(u ^*) :u U _A are homogeneous reductive spaces. IfA is aC ^* algebra,e the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe by invertible elements ofA can be imbedded inAA in such a way thate is carried to 1 1 and the orbit ofe to a homogeneous reductive space and an analytic submanifold ofAA.     

Composition operators from large weighted Hardy spaces into the Dirichlet space

Given a large weighted Hardy space we show there exists a composition operatorC with that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.This research was supported in part by a summer stipend from Bellarmine College.     

The Structure of a Class of K-contact Manifolds

In this paper we study a class of K-contact manifolds, namely -conformally flat K-contact manifolds and we show that a compact -conformally flat K-contact manifold with regular contact vector field is a principal S¹-bundle over an almost Kaehler space of constant holomorphic sectional curvature.     

Solution of the Truncated Parabolic Moment Problem

Given real numbers with ₀₀ >0 , the truncated parabolic moment problem for entails finding necessary and sufficient conditions for the existence of a positive Borel measure , supported in the parabola p(x, y) = 0, such that We prove that admits a representing measure (as above) if and only if the associated moment matrix is positive semidefinite, recursively generated and has a column relation p(X, Y) = 0, and the algebraic variety () associated to satisfies card In this case, admits a rank -atomic (minimal) representing measure.Submitted: August 25, 2003     

Quasi-coherence of Hardy spaces in several complex variables

In this paper, we prove that the Hardy spaceH ^p (), 1p<, over a strictly pseudoconvex domain in ⁿ with smooth boundary is quasi-coherent. More precisely, we show that Toeplitz tuplesT with suitable symbols onH ^p () have property (). This proof is based on a well known exactness result for the tangential Cauchy-Riemann complex.     

Some homological properties of commutative semitrivial ring extensions

LetR be a commutative ring with 1 andM anR-module. If:M _R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM ^*, where the isomorphism is given by the adjoint of.     

C 1 changes of variable: Beurling-Helson type theorem and Hörmander conjecture on Fourier multipliers

We prove that if aC ¹ smooth change of variable : generates a bounded composition operatorff° in the spaceA _p()=L ^p ,p2, then is linear (affine).We also prove that for a nonlinearC ¹ mapping , the norms of exponentialse ⁱ as Fourier multipliers inL ^p () tend to infinity (,||). In both results the condition C ¹ is sharp, it cannot be replaced by the Lipschitz condition.     

Small compact perturbation of strongly irreducible operators

An operatorT onH is called strongly irreducible ifT is not similar to any reducible operators. In this paper, we shall say yes to answer the following question raised by D. A. Herrero.Given an operatorT with connected spectrum (T) and a positive number , can we find a compact operatorK with K < such thatT+K is strongly irreducible?Supported by National Natural Science Foundation of China(19901011), Mathematical Center of State Education Commission of China and 973 Project of China     

Algorithmes de calcul du maximum des formes quadratiques sur la boule unité de la norme du maximum

Résumé Certaines méthodes directes et indirectes pour le calcul de Max {x ^t Ax, (x)1} sont étudiées.Les méthodes directes sont basées sur les propriétés particulières des normes ₁, ₂ et . Ces méthodes sont très simples mais ne s'appliquent qu'à certaines familles de matrices.La méthode indirecte est la méthode autoduale introduite dans [25, 26] avec = ₁. Dans ce cas, le choix du vecteur initial pour qu'il y ait convergence vers une solution optimale est largement discuté.

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Some methods for computing the maximum of quadratic from on the unit ball of the maximum norm

Summary Some direct and indirect methods are studied for computing Max {x ^t Ax, (x)1} whereA is symmetric definite positive.Direct methods are constructed using particular properties of ₁, ₂, norms. These methods are very simple, but uniquely suitable to certains families of matrices.The indirect method is the autodual method, introduced in [25, 26, 29] with = ₁. In this case the problem of choosing an initial vector so that convergence of the iterative sequence occurs to an optimal solution is largely discussed.

     

φ-Factors for Function Seminorms

Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier.     

Weighted Bergman Spaces and Carleson Measures on the Unit Ball of Cn

Let be a normal function on [0, 1), B _n the unit ball of C ⁿ , and A ^p (B _n ) the weighted Bergman spaces on B _n with weight . The purpose of this paper is to discuss some relations among A ^p (B _n ), weighted Bergman kernels, and Carleson measures on B _n .