Measurable Functions on Hilbert Spaces

2004 ◽  
pp. 525-557
Author(s):  
Iosif Il’ich Gihman ◽  
Anatoliĭ Vladimirovich Skorokhod
Keyword(s):  
Hilbert Spaces ◽  
Measurable Functions

scholarly journals PIP-Space Valued Reproducing Pairs of Measurable Functions

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 52 ◽  
Author(s):  
Jean-Pierre Antoine ◽  
Camillo Trapani
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Measure Space ◽  
Abstract Space ◽  
Initial Space ◽  
Measurable Functions ◽  
Continuous Frames

We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space Y as superpositions of weakly measurable functions belonging to a space Z : = Z ( X , μ ) , where ( X , μ ) is a measure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbert spaces; (ii) Y is a Hilbert space, but Z is a pip-space; (iii) Y and Z are both pip-spaces. It is shown, in particular, that the requirement that a pair of measurable functions be reproducing strongly constrains the structure of the initial space Y. Examples are presented for each case.

APPLICATIONS OF KATO'S INEQUALITY TO OPERATOR-VALUED INTEGRALS ON HILBERT SPACES

2013 ◽  
Vol 06 (04) ◽  
pp. 1350059
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Complex Hilbert Space ◽  
Bochner Integral ◽  
Measurable Functions ◽  
Kato’S Inequality ◽  
Operator Exponential

By the use of the celebrated Kato's inequality we obtain in this paper some inequalities for operator-valued integrals on a complex Hilbert space H. Among others, we show that [Formula: see text] for any x, y ∈ H, provided [Formula: see text] and p : E → [0, ∞) are μ-measurable functions on E and such that [Formula: see text] and [Formula: see text] are Bochner integrable on E for some α ∈ [0, 1]. Natural applications for various norms and numerical radii associated with the Bochner integral of operator-valued functions and some examples for the operator exponential are presented as well.

Gaussian Hilbert Spaces

1997 ◽  
Author(s):  
Svante Janson
Keyword(s):  
Hilbert Spaces

On split equality monotone Yosida variational inclusion and fixed point problems for countable infinite families of certain nonlinear mappings in Hilbert spaces

2020 ◽  
Vol Accepted ◽  
Author(s):  
Oluwatosin Temitope Mewomo ◽  
Hammed Anuoluwapo Abass ◽  
Chinedu Izuchukwu ◽  
Olawale Kazeem Oyewole
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Variational Inclusion ◽  
Nonlinear Mappings

CLASSIFICATIONS OF BOREL MEASURABLE FUNCTIONS

1994 ◽  
Vol 20 (2) ◽  
pp. 407
Author(s):  
Morayne
Keyword(s):  
Measurable Functions ◽  
Borel Measurable

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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