Hilbert lattices: New results and unsolved problems

1990 ◽  
Vol 20 (5) ◽  
pp. 529-559 ◽  
Author(s):  
Herbert Gross
Keyword(s):  
Hilbert Lattices

A Hilbert Lattice With a Small Automorphism Group

1987 ◽  
Vol 30 (2) ◽  
pp. 182-185 ◽  
Author(s):  
Urs-Martin Künzi
Keyword(s):  
Automorphism Group ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Hilbert Lattice ◽  
Hilbert Lattices

AbstractWe construct an orthomodular inner product space to answer the questions posed by R. P. Morash in his paper "Angle bisection and orthoautomorphisms in Hilbert lattices" [6]. For example we show that every automorphism of the Hilbert lattice belonging to our inner product space has the property, that no atom is orthogonal to its image.

scholarly journals Принцип Канторовича в действии: AW∗-модули и инъективные банаховы решетки

2012 ◽  
Author(s):  
A.G. Kusraev
Keyword(s):  
Banach Lattices ◽  
Transfer Principle ◽  
Value Transfer ◽  
Heuristic Principle ◽  
The Relationship ◽  
Hilbert Lattices

Making use of Boolean valued representation it is proved that Kaplansky-Hilbert lattices and injective Banach lattices may be produced from each other by means of the convexification procedure. The relationship between the Kantorovich's heuristic principle and the Boolean value transfer principle is also discussed.

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