Orthogonal least squares solutions for linear operators.
Partial isometries and EP elements in rings with involution.
Perturbation of the generalized Drazin inverse.
Powers of operators
Proper subspaces and compatibility
Let 𝓔 be a Banach space contained in a Hilbert space 𝓛. Assume that the inclusion is continuous with dense range. Following the terminology of Gohberg and Zambickiĭ, we say that a bounded operator on 𝓔 is a proper operator if it admits an adjoint with respect to the inner product of 𝓛. A proper operator which is self-adjoint with respect to the inner product of 𝓛 is called symmetrizable. By a proper subspace 𝓢 we mean a closed subspace of 𝓔 which is the range of a proper projection. Furthermore,...
Properties and applications of Tauberian operators.
Tauberian operators, which appeared in response to a problem in summability [GaW, KW] have found application in several situations: factorization of operators [DFJP], preservation of isomorphic properties of Banach spaces [N, NR], equivalence between the Radon-Nikodym property and the Krein-Milman property [Sch], and generalized Fredholm operators [Ta, Y].This paper is a survey of the main properties and applications of Tauberian operators.
Properties of Some Norm Related Functions of Unbounded Linear Operators.
Proprietà spettrali di certi operatori lineari non compatti
Pták homomorphism theorem revisited
Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.
q-deformed circularity for an unbounded operator in Hilbert space
The notion of strong circularity for an unbounded operator is introduced and studied. Moreover, q-deformed circularity as a q-analogue of circularity is characterized in terms of the partially isometric and the positive parts of the polar decomposition.
Quasi-similarity of contractions having a 2×1 characteristic function.
Quotient spaces defined by linear relations
Range of operators and regularity of solutions
Regular operators on partial inner product spaces
Regularity of domains of parameterized families of closed linear operators
The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) for t ∈ . Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter;...
Relatively open operators and the ubiquitous concept.
A linear operator T: D(T) ⊂ X → Y, when X and Y are normed spaces, is called ubiquitously open (UO) if every infinite dimensional subspace M of D(T) contains another such subspace N for which T|N is open (in the relative sense). The following properties are shown to be equivalent: (i) T is UO, (ii) T is ubiquitously almost open, (iii) no infinite dimensional restriction of T is injective and precompact, (iv) either T is upper semi-Fredholm or T has finite dimensional range, (v) for each infinite...
Relatively tauberian resolvent operators.
Remark on linear equations in Banach space
Remark on sums of complemented subspaces
Representation and duality of multiplication operators on archimedean Riesz spaces