Abstract: Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some linear operators in spaces with an indefinite metric references. People with open minded will always try to seek for the new things and information from many sources. On the contrary, people with closed mind will always think that they can do it by their principals. So, what kind of person are you?

Abstract: In abstract spaces, we consider certain constrained controllability and approximate controllability properties of a nonlinear system that can be deduced from various controllability properties of its associated linear system. Several examples involving partial differential operators and functional delay operators are given to illustrate the theory.

Abstract: We investigate how compact operators behave under J and K interpolation methods for N spaces and two parameters. First we study those methods: relationship with those already existing in the literature, estimates for the norms of interpolated operators, examples, characterization as Aronszajn-Gagliardo functors,.... We also describe the relationship between Sparr and Fernandez methods and we derive sharp estimates for the norms of interpolated operators in Fernandez' case. Then we investigate the behaviour of compact operators. We begin with the case when one of the N-tuples reduces to a single Banach space, and later we treat the general case by means of the approach developed in [8].

Abstract: The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact permits us to describe the set of solutions to the string equation in terms of moduli spa- ces of algebraic curves,however the direct description is much simpler. Some results are obtained for the superanalog to the string equation where $P$ and $Q$ are considered as superdifferential operators. It is proved that this equation is invariant with respect to Manin-Radul, Mulase-Rabin and Kac-van de Leur KP-hierarchies.

Abstract: Preface 1. Preliminaries 2. Bounded derivations 3. Unbounded derivations 4. C*-dynamical systems Index.

Abstract: In this paper we study rings of differential operators for modules of covariants for one-dimensional tori. In particular we analyze when they are Morita equivalent, when they are simple, and when they have finite global dimension. As a side result we obtain an extension of the Bernstein-Beilinson equivalence to weighted projective spaces.

Abstract: Dissipative Schrodinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.

Abstract: Let X = LP(Ii), where 1 ? p R,, is a uniformly bounded, strongly continuous representation of G in X by separation-preserving operators (for instance, by positivity-pre- serving operators). We show that R transfers to X strong type maximal estimates for sequences of convolution operators defined on LP(G). If R also has a uniformly bounded version in L2(%t), then R will transfer to LP((t) strong type bounds for maximal operators defined by sequences of multipliers which are continuous on the dual group G. These theo- rems, which cease to be valid if the separation-preserving hypothesis is removed, provide strong type maximal operator counterparts for the corresponding single operator theorems of Coifman-Weiss transference theory. One consequence of the second theorem described above is a maximal.theorem counterpart of the Homomorphism Theorem for Sin- gle Multiplier Transforms.

Abstract: In this paper the study of a functional calculus for subnormal ntuples is initiated and the minimal normal extension problem for this functional calculus is explored. This problem is shown to be equivalent to a mean approximation problem in several complex variables which is solved. An analogous uniform approximation problem is also explored. In addition these general results are applied together with The Area and the The Coarea Formula from Geometric Measure Theory to operators on Bergman spaces and to the tensor product of two subnormal operators. The minimal normal extension of the tensor product of the Bergman shift with itself is completely determined. An n-tuple of commuting operators S = (S1, . . ., Sn) on a Hilbert space Z is subnormal if there is an n-tuple N = (Nl, ..., Nn) of commuting normal operators on a Hilbert space Z that contains Z such that for 1 < j < n, Nj}° C }° and Sj = Njlt. For any commuting n-tuple of operators S there is a notion of spectrum, the Taylor spectrum of S [30] (also see [12]), denoted by v(S). This spectrum is a nonempty compact subset of (Un. In this general theory it is possible to define +(S) for any function + analytic in a neighborhood of v(S). This functional calculus generalizes the usual Riesz functional calculus for a single operator. When S is assumed to be a subnormal n-tuple, however, a much richer functional calculus is possible. In this case 0(S) can be defined for functions 0 that are weak* limits of analytic functions and 0(S) becomes a subnormal operator. The central question in this development is "What are the properties of this operator 0(S) and what are the relations between the operator and the function X ?" More generally, if S is an n-tuple and Xl, . . ., Xq are analytic functions defined in a neighborhood of the Taylor spectrum of S, then 0(S)-(0l (S), .... Xq(S)) is a commuting q-tuple of operators. If S is subnormal, then 0(S) can be defined for X = (0l, ..., Xq) consisting of functions that are weak* limits Received by the editors January 31, 1989 and, in revised form, July 6, 1989. 1980 Mathematics Subject Classification (1985 Revision). Primary 47B20, 47A60; Secondary 32A35, 47B38. The results here were delivered in a talk at the American Mathematical Society Summer Institute in Operator Theory held at the University of New Hampshire in July 1988. During the preparation of this paper partial support was furnished by National Science Foundation grant DMS 87-00835. (32)1991 American Mathematical Society 0002-9947/91 $1.00 + $.25 per page

Abstract: Let X be a compact Hausdorff space, let E be a Banach space, and let C(X,E) stand for the Banach space of E-valued continuous functions on X under the uniform norm. In this paper we characterize integral operators (in the sense of Grothendieck) on C(X,E) spaces in terms of their representing vector measures. This is then used to give some applications to nuclear operators on C(X,E) spaces

Abstract: The Singular Integral Operators Method is presented for the formulation of the two-dimensional elasto-plastic stress analysis. The formulation of the two-dimensional elasto-plastic problem is stated, by applying the fundamental solutions for an isotropic solid. The most interesting features of this method are the much smaller systems of equations and considerable reduction in the data required to run the elasto-plastic problem. An application is presented, to the determination of the stress field in the neighborhood of a circular hole under internal pressure in an infinite and isotropic solid. A second application is stated, to the determination of the plastic behaviour of a square block compressed by two opposite perfectly rough rigid punches in plane strain.

Abstract: Injective matricial operator spaces have been classified up to Banach space isomorphism in [20]. The result is that every such space is isomorphic to l∞, l2, B(l2), or a direct sum of such spaces. A more natural project, given the matricial nature of the definitions involved, would be the classification of such spaces up to completely bounded isomorphism. This was done for injective von Neumann algebras in [6] and for injective operator systems (i.e. unital injective operator spaces) in [19]. It turns out that the spaces l∞ and B(l2) are in a natural way uniquely characterized up to completely bounded isomorphism. However, as shown in [20], a problem arises in the case of l2. For there are two injective operator spaces which are each isometrically isomorphic to l2 but not completely boundedly isomorphic to each other. We shall resolve this problem by showing that these are the only two possibilities, in the sense that any injective operator space which is isometric to l2 is completely isometric to one of them. (See Corollary 3 below.) The Hilbert spaces in von Neumann algebras investigated in [17], [13] turn out to be injective matricial operator spaces and are therefore completely isometric to one of our two examples. Another Hilbert space in B(l2) which has been much studied in operator theory, complex analysis and physics is the Cartan factor of type IV [10]. This is the complex linear span of a spin system and generates the Fermion C*-algebra ([3], §5·2). We show that a Cartan factor of type IV is not even completely boundedly isomorphic to an injective matricial operator space. One curious property of all the aforementioned Hilbert spaces is that every bounded operator on them is actually completely bounded, a fact that is crucial in our proofs.

Abstract: When (Tn) is a sequence of selfadjoint random operators on a separable Hilbert space H converging almost surely to T, and converges in distribution to a random operator U, we give explicitly the asymptotic joint distribution of all the eigenelements of Tn (eigenvalues, eigenvectors and eigenprojectors) as a function of U. The results are obtained for real or complex operators, and for eigenvalues which arc simple or not. They have many applications in Multi-variate Analysis; for example, the asymptotic studies of Principal Component Analysis (real or complex), Canonical Analysis, Discriminant Analysis, Correspondence Analysis, Functional models.

Abstract: We introduce the class of weak Schur spaces, i.e., Banach lattices in which relatively weakly compact sets and almost order bounded sets coincide. There follows a detailed study of Banach lattices in which every semi-normalized, order bounded, weakly null sequence contains a subsequence satisfying a lower, resp. an upper, 2-estimate. From the previous results we obtain conditions under which non-Dunford-Pettis operators between certain classes of Banach lattices fix a copy of l2.

Abstract: A special class of normal operators acting in spaces with indefinite scalar products is studied. The operators from this class are characterized by the property that, in a natural basis, their matrices have diagonal block-Toeplitz forms. The relations between polynomials of self-adjoint operators and operators from this class are established.

Abstract: This note deals with a class of convolution operators of the first kind on a finite interval. Necessary and sufficient conditions for such an operator to be Fredholm are given. The argument is based on a process of reduction of convolution-type operators on a finite interval to operators of the same type on the half line.