Hilbert spaces have the strong Banach-stone property for Bochner spaces

1987 ◽  
Vol 196 (4) ◽  
pp. 511-515 ◽  
Author(s):  
P. Greim ◽  
J. E. Jamison
Keyword(s):  
Hilbert Spaces ◽  
Stone Property

scholarly journals Hilbert spaces have the Banach-Stone property for Bochner spaces

1983 ◽  
Vol 27 (1) ◽  
pp. 121-128 ◽  
Author(s):  
Peter Greim
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Type Theorem ◽  
Finite Measure ◽  
Linear Isometry ◽  
Measure Spaces ◽  
Stone Type ◽  
Stone Property

Let (ωi, σi, μi.) be two positive finite measure spaces, V a non-zero Hilbert space, and 1 ≤ p < ∞, p # 2. In this article it is shown that each surjective linear isometry between the Bochner spaces induces a Boolean isomorphism between the measure algebras , thus generalizing a result of Cambern's for separable Hilbert spaces.This Banach–Stone type theorem is achieved via a description of the Lp-structure of .

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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