Abstract
We consider the class of the continuous L2,1 linear operators in L2 that are sums of the operators of multiplication by bounded measurable functions and the operators sending the unit ball of L2 into a compact subset of L1. We prove that a functional equation with an operator from L2,1 is equivalent to an integral equation with kernel satisfying the Carleman condition. We also prove that if T ∈ L2,1 and VTV−1 ∈ L2,1 for all unitary operators V in L2 then T = α1 + C, where α is a scalar, 1 is the identity operator in L2, and C is a compact operator in L2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.