scholarly journals Strictly cyclic operator algebras

1991 ◽  
Vol 325 (1) ◽  
pp. 73-86 ◽  
Author(s):  
John Froelich
Keyword(s):  
Operator Algebras ◽  
Cyclic Operator

scholarly journals Strictly Cyclic Functionals, Reflexivity, and Hereditary Reflexivity of Operator Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Quanyuan Chen ◽  
Xiaochun Fang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Operator Algebra ◽  
Operator Algebras ◽  
Reflexive Banach Space ◽  
Cyclic Operator ◽  
Abelian Subalgebra ◽  
Cyclic Vectors ◽  
Reflexive Algebra

This paper is concerned with strictly cyclic functionals of operator algebras on Banach spaces. It is shown that ifXis a reflexive Banach space andAis a norm-closed semisimple abelian subalgebra ofB(X)with a strictly cyclic functionalf∈X∗, thenAis reflexive and hereditarily reflexive. Moreover, we construct a semisimple abelian operator algebra having a strictly cyclic functional but having no strictly cyclic vectors. The hereditary reflexivity of an algbra of this type can follow from theorems in this paper, but does not follow directly from the known theorems that, if a strictly cyclic operator algebra on Banach spaces is semisimple and abelian, then it is a hereditarily reflexive algebra.

scholarly journals Strictly cyclic operator algebras

1971 ◽  
Vol 39 (3) ◽  
pp. 717-726 ◽  
Author(s):  
Alan Lambert
Keyword(s):  
Operator Algebras ◽  
Cyclic Operator

scholarly journals Hereditarily strictly cyclic operator algebras

1991 ◽  
Vol 41 (3) ◽  
pp. 507-511
Author(s):  
Subhash Chander Arora ◽  
Pawan Bala
Keyword(s):  
Operator Algebras ◽  
Cyclic Operator
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