871 research outputs found
Remarks on tree-level topological string theories
A few observations concerning topological string theories at the string-tree
level are presented: (1) The tree-level, large phase space solution of an
arbitrary model is expressed in terms of a variational problem, with an
``action'' equal, at the solution, to the one-point function of the puncture
operator, and found by solving equations of Gauss-Manin type; (2) For
Landau-Ginzburg models, an extension to large phase space of the usual residue
formula for three-point functions is given.Comment: LaTeX2e, 8 page
Dense definiteness and boundedness of composition operators in -spaces via inductive limits
The questions of dense definiteness and boundedness of composition operators
in -spaces are studied by means of inductive limits of operators. Methods
based on projective systems of measure spaces and inductive limits of
-spaces are developed. Illustrative examples are presented
Quantum Spaces: Notes and Comments on a Lecture by S. L. Woronowicz
These notes are based on a lecture given by S. L. Woronowicz at the Institute
of Mathematics, Polish Academy of Sciences.Comment: 11 pages, LaTe
Quantum Principal Fiber Bundles: Topological Aspects
We introduce the notion of locally trivial quantum principal bundles. The
base space and total space are compact quantum spaces (unital
-algebras), the structure group is a compact matrix quantum group.
We prove that a quantum bundle admits sections if and only if it is trivial.
Using a quantum version of \v{C}ech cocycles, we obtain a reconstruction
theorem for quantum principal bundles. The classification of bundles over a
given quantum space as a base space is reduced to the corresponding problem,
but with an ordinary classical group playing the role of structure group. Some
explicit examples are considered.Comment: 29 pages, LaTeX, IM PAN preprint # 51
New properties of Cauchy and event horizons
We present several recent results concerning Cauchy and event horizons. In
the first part of the paper we review the differentiablity properties of the
Cauchy and the event horizons. In the second part we discuss compact Cauchy
horizons and summarize their main properties.Comment: 11 pages, Talk at 2nd World Congress on Non-linear Analysis (July
2000, Catania, Italy
Unbounded composition operators via inductive limits: cosubnormal operators with matrix symbols. II
The paper deals with unbounded composition operators with infinite matrix
symbols acting in -spaces with respect to the gaussian measure on
. We introduce weak cohyponormality classes
\EuScript{S}_{n,r}^* of unbounded operators and provide criteria for the
aforementioned composition operators to belong to \EuScript{S}_{n,r}^*. Our
approach is based on inductive limits of operators
Unbounded composition operators via inductive limits: cosubnormals with matrical symbols
We prove, by use of inductive techniques, that assorted unbounded composition
operators in -spaces with matrical symbols are cosubnormal.Comment: 8 page
Quasinormal extensions of subnormal operator-weighted composition operators in -spaces
We prove the subnormality of an operator-weighted composition operator whose
symbol is a transformation of a discrete measure space and weights are
multiplication operators in -spaces under the assumption of existence of a
family of probability measures whose Radon-Nikodym derivatives behave regular
along the trajectories of the symbol. We build the quasinormal extension which
is a weighted composition operator induced by the same symbol. We give
auxiliary results concerning commutativity of operator-weighted composition
operators with multiplication operators
Generalized strong curvature singularities and weak cosmic censorship in cosmological space-times
This paper is a further development of the approach to weak cosmic censorship
proposed by the authors in Ref. 5. We state and prove a modified version of
that work's main result under significantly relaxed assumptions on the
asymptotic structure of space--time. The result, which imposes strong
constraints on the occurrence of naked singularities of the strong curvature
type, is in particular applicable to physically realistic cosmological models.Comment: Latex, 7 pages, no figures, to be published in Mod. Phys. Lett.
A note on -hyperreflexivity of Toeplitz-harmonic subspaces
The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an
isometry or a quasinormal operator is shown. The -hyperreflexivity of the
tensor product of a -hyperreflexive
decomposable subspace and an abelian von Neumann algebra
is established
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