Generalized eigenfunctions of relativistic Schrödinger operators. I.
Generalized eigenfunctions of relativistic Schrödinger operators in two dimensions.
Generalized Eigenvector Expansion for Weakly Perturbated Discrete Operators
Generalized Fock spaces, interpolation, multipliers, circle geometry.
By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e-Q(z), where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle C in C. We consider the problem of interpolation between two Fock spaces. If C0 and C1 are the corresponding circles, one is led to consider the pencil of circles generated by C0 and C1....
Generalized fractional linear transformations: convexity and compactness of the image and the pre-image; applications.
The convexity and compactness in the weak operator topology of the image and pre-image of a generalized fractional linear transformation is established. As an application the exponential dichotomy of solutions to evolution problems of the parabolic type is proved.
Generalized Gram-Hadamard inequality.
Generalized Hardy's inequality
Generalized induced norms
Let be a norm on the algebra of all matrices over . An interesting problem in matrix theory is that “Are there two norms and on such that for all ?” We will investigate this problem and its various aspects and will discuss some conditions under which .
Generalized invariant subspaces for linear operators
Generalized inverses in C*-algebras II
Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.
Generalized limits and a mean ergodic theorem
For a given linear operator L on with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on and , the definition of L-limit reduces to Lorentz’s definition of σ-limit, which is described by means of Banach limits on . We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version of the abstract...
Generalized quadratic operators and perturbations
We provide a complete description of the perturbation class and the commuting perturbation class of all generalized quadratic bounded operators with respect to a given idempotent bounded operator in the context of complex Banach spaces. Furthermore, we give simple characterizations of the generalized quadraticity of linear combinations of two generalized quadratic bounded operators with respect to a given idempotent bounded operator.
Generalized resolvents and spectrum for a certain class of perturbed symmetric operators.
Generalized spectral perturbation and the boundary spectrum
By considering arbitrary mappings from a Banach algebra into the set of all nonempty, compact subsets of the complex plane such that for all , the set lies between the boundary and connected hull of the exponential spectrum of , we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.
Generalized Weyl's theorem and quasi-affinity
A bounded operator T ∈ L(X) acting on a Banach space X is said to satisfy generalized Weyl's theorem if the complement in the spectrum of the B-Weyl spectrum is the set of all eigenvalues which are isolated points of the spectrum. We prove that generalized Weyl's theorem holds for several classes of operators, extending previous results of Istrăţescu and Curto-Han. We also consider the preservation of generalized Weyl's theorem between two operators T ∈ L(X), S ∈ L(Y) intertwined or asymptotically...
Generating real maps on a biordered set.
Generating real maps on a biordered set
Several authors have defined operational quantities derived from the norm of an operator between Banach spaces. This situation is generalized in this paper and we present a general framework in which we derivate several maps from an initial one , where is a set endowed with two orders, and , related by certain conditions. We obtain only three different derivated maps, if the initial map is bounded and monotone.
Generic properties of iterated function systems with place dependent probabilities.
Generic properties of learning systems
It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
Generic properties of von Kármán equations