Note that there are examples of strictly singular operators whose adjoints are neither strictly singular nor strictly cosingular ( see Plichko, 2004 ).
2.
Petermichl won the Salem Prize for 2006 " for her work on several crucial impacts to the theory of vector valued singular operators ".
3.
The class of inessential operators, which properly contains the class of strictly singular operators, is the " perturbation class " for Fredholm operators.
4.
Denote by \ mathcal { FSS } ( X, Y ) the set of all finitely strictly singular operators in B ( X, Y ).
5.
He gained particular attention with his work on Analysis on local Dirichlet spaces, 1993-1995, where he introduced geometric concepts for the investigation of stochastic processes and carried over methods from elliptic regularity theory to singular operators on abstract spaces, as well as with his pioneering work on synthetic Ricci bounds for metric measure spaces.
6.
Strictly singular operators can be viewed as a generalization of spectrum \ sigma ( T ) satisfies the following properties : ( i ) the cardinality of \ sigma ( T ) is at most countable; ( ii ) 0 \ in \ sigma ( T ) ( except possibly in the trivial case where " X " is finite-dimensional ); ( iii ) zero is the only possible limit point of \ sigma ( T ); and ( iv ) every nonzero \ lambda \ in \ sigma ( T ) is an eigenvalue.
मोबाइल