weyl theorem
Recently Published Documents


TOTAL DOCUMENTS

42
(FIVE YEARS 0)

H-INDEX

7
(FIVE YEARS 0)

2017 ◽  
Vol 50 (1) ◽  
pp. 42-50 ◽  
Author(s):  
Artur Giżycki ◽  
Leszek Pysiak

Abstract We study the representations of transitive transformation groupoids with the aim of generalizing the Mackey theory. Using the Mackey theory and a bijective correspondence between the imprimitivity systems and the representations of a transformation groupoid we derive the irreducibility theory. Then we derive the direct sum decomposition for representations of a groupoid together with the formula for the multiplicity of subrepresentations. We discuss a physical interpretation of this formula. Finally, we prove the claim analogous to the Peter-Weyl theorem for a noncompact transformation groupoid. We show that the representation theory of a transitive transformation groupoids is closely related to the representation theory of a compact groups.


2015 ◽  
Vol 7 (4) ◽  
pp. 266-275 ◽  
Author(s):  
C. Carmeli ◽  
R. Fioresi ◽  
S. Kwok
Keyword(s):  

2015 ◽  
Vol 95 ◽  
pp. 144-158 ◽  
Author(s):  
C. Carmeli ◽  
R. Fioresi ◽  
S. Kwok
Keyword(s):  

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1641-1652 ◽  
Author(s):  
M.H.M. Rashid

An operator T acting on a Banach space X obeys property (R) if ?0a(T) = E0(T), where ?0a(T) is the set of all left poles of T of finite rank and E0(T) is the set of all isolated eigenvalues of T of finite multiplicity. In this paper we introduce and study two new properties (S) and (gS) in connection with Weyl type theorems. Among other things, we prove that if T is a bounded linear operator acting on a Banach space, then T satisfies property (R) if and only if T satisfies property (S) and ?0(T) = ?0a(T), where ?0(T) is the set of poles of finite rank. Also we show if T satisfies Weyl theorem, then T satisfies property (S). Analogous results for property (gS) are given. Moreover, these properties are also studied in the frame of polaroid operator.


2013 ◽  
Vol 64 (9) ◽  
pp. 1464-1474 ◽  
Author(s):  
M. H. M. Rashid
Keyword(s):  

2011 ◽  
Vol 226 (6) ◽  
pp. 4776-4795 ◽  
Author(s):  
Dikran Dikranjan ◽  
Dmitri Shakhmatov
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document