Compact operators and the singular value expansion

2014 ◽  
Vol 96 (3) ◽  
pp. 386-395 ◽  
Author(s):  
G. RAMESH

AbstractIn this paper we prove a structure theorem for the class of $\mathcal{AN}$-operators between separable, complex Hilbert spaces which is similar to that of the singular value decomposition of a compact operator. Apart from this, we show that a bounded operator is $\mathcal{AN}$ if and only if it is either compact or a sum of a compact operator and scalar multiple of an isometry satisfying some condition. We obtain characterizations of these operators as a consequence of this structure theorem and deduce several properties which are similar to those of compact operators.


2012 ◽  
Vol 437 (10) ◽  
pp. 2516-2522 ◽  
Author(s):  
Wasim Audeh ◽  
Fuad Kittaneh

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