Real linear operators arise in a range of applications of mathematical physics. In this paper, basic properties of real linear operators are studied and their spectral theory is developed. Suitable extensions of classical operator theoretic concepts are introduced. Providing a concrete class, real linear multiplication operators are investigated and, motivated by the Beltrami equation, related ...

Abstract The properties of being shift invariant and reflexive or transitive in the case space (asymmetric) truncated Toeplitz operators, dual operators are investigated. Most results obtained new even for symmetric case. A characterization asymmetric is also given.

ABSTRACT. Let (a, 6) be any open subinterval of the reals which contains the origin and let 33 denote the family of all distributions on [a, b) which are regular in some interval (e, 0), where e < 0. Then S is a commutative algebra: Multiplication is defined so that, when restricted to those distributions on (a, b) whose supports are contained in [0, b), it is ordinary convolution. Also, S) can...