On the existence of a Hilbert-space model for finite-valued observables

1992 ◽  
Vol 107 (12) ◽  
pp. 1413-1426 ◽  
Author(s):  
A. Fedullo
Keyword(s):  
Hilbert Space ◽  
Space Model

A proof of Hartman's theorem on compact Hankel operators

1975 ◽  
Vol 78 (3) ◽  
pp. 447-450 ◽  
Author(s):  
F. F. Bonsall ◽  
S. C. Power
Keyword(s):  
Hilbert Space ◽  
Compact Operator ◽  
Hankel Operator ◽  
Hankel Operators ◽  
Unilateral Shift ◽  
Space Model ◽  
Model Free ◽  
Multiplicity One ◽  
Image Position ◽  
Algebra Of Operators

Let U be a unilateral shift of arbitrary (perhaps uncountable) multiplicity on a Hilbert space. Following Rosenblum (5), an operator A is said to be a Hankel operator relative to U ifHartman (2) has characterized the compact Hankel operators relative to the unilateral shift of multiplicity one as the Hankel operators with symbol in H∞ + C(T). Using the usual function space model for representing the unilateral shift, Page ((4), theorem 10) has extended Hartman's theorem to unilateral shifts of countable multiplicity. We give a model-free proof of Hartman's theorem which applies to shifts of arbitrary multiplicity. The proof turns on the observation that a compact operator acts compactly on a certain algebra of operators.

$$\bar{p}N$$ Scattering with Annihilation Channel in an Extended Hilbert Space Model

1995 ◽  
pp. 409-414
Author(s):  
Yu. A. Kuperin ◽  
S. B. Levin ◽  
Yu. B. Melnikov ◽  
E. A. Yarevsky
Keyword(s):  
Hilbert Space ◽  
Annihilation Channel ◽  
Space Model

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space

Positional Estimation Within a Latent Space Model for Networks

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 24-33 ◽  
Author(s):  
Susan Shortreed ◽  
Mark S. Handcock ◽  
Peter Hoff
Keyword(s):  
Random Effects ◽  
Network Data ◽  
Random Effects Models ◽  
Space Model ◽  
Network Analyses ◽  
Recent Advances ◽  
Latent Space ◽  
Latent Space Model ◽  
Modeling Data

Recent advances in latent space and related random effects models hold much promise for representing network data. The inherent dependency between ties in a network makes modeling data of this type difficult. In this article we consider a recently developed latent space model that is particularly appropriate for the visualization of networks. We suggest a new estimator of the latent positions and perform two network analyses, comparing four alternative estimators. We demonstrate a method of checking the validity of the positional estimates. These estimators are implemented via a package in the freeware statistical language R. The package allows researchers to efficiently fit the latent space model to data and to visualize the results.

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