Maps on Idempotent Operators with Infinite-Dimensional Kernel

2019 ◽  
Vol 46 (1) ◽  
pp. 263-270
Author(s):  
Lin Chen ◽  
Juan Li ◽  
Fangyan Lu
Keyword(s):  
Infinite Dimensional ◽  
Idempotent Operators

Maps Preserving Complementarity of Closed Subspaces of a Hilbert Space

2014 ◽  
Vol 66 (5) ◽  
pp. 1143-1166 ◽  
Author(s):  
Lucijan Plevnik ◽  
Peter Šemrl
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Idempotent Operators

AbstractLet and be infinite-dimensional separable Hilbert spaces and Lat the lattice of all closed subspaces oh . We describe the general form of pairs of bijective maps ϕ, Ψ : Lat → Lat having the property that for every pair U, V ∊ Lat we have . Then we reformulate this theorem as a description of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known structural results for maps on idempotents are easy consequences.

Criterion of cyclically compactness infinite-dimensional normed module

2018 ◽  
Vol 2018 (3) ◽  
pp. 51-62
Author(s):  
V.I. Chilin ◽  
J.A. Karimov
Keyword(s):  
Infinite Dimensional ◽  
Normed Module

Distribution and Analytical Measure on Infinite Dimensional Spaces

2018 ◽  
Vol 483 (1) ◽  
pp. 7-10
Author(s):  
A. Belyaev ◽  
◽  
O. Smolyanov ◽  
◽  
Keyword(s):  
Infinite Dimensional
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