26 citations · 45 across the 10 of their papers we have counts for
9 papers · 1 filter
A geometric characterization of range-kernel complementarity
Dimosthenis Drivaliaris, Nikos Yannakakis
We show that a bounded linear operator on a Banach space with closed range has range-kernel complementarity if and only if its generalized amplitude is less than . An applicatio…
The spectrum of the restriction to an invariant subspace
Dimosthenis Drivaliaris, Nikos Yannakakis
Let be a Banach space, and be an invariant subspace of . We present an alternative proof that, if the spectrum of the restriction of to contains a po…
The angle along a curve and range-kernel complementarity
Dimosthenis Drivaliaris, Nikos Yannakakis
In this paper, we define the angle of a bounded linear operator along an unbounded path emanating from the origin and use it to characterize range-kernel complementarity. In pa…
The angle of an operator and range and kernel complementarity
Dimosthenis Drivaliaris, Nikos Yannakakis
We show that if the angle of a bounded linear operator on a Banach space, with closed range and closed sum of its range and kernel, is less than , then its range and kernel are…
Density of smooth functions in variable exponent Sobolev spaces
Thanasis Kostopoulos, Nikos Yannakakis
We show that if , then a sufficient condition for the density of smooth functions with compact support, in the variable exponent Sobolev space $W^{1,p(\cdot)}(\mathbb R^…
Stampacchia's property, self-duality and orthogonality relations
Nikos Yannakakis
We show that if the conclusion of the well known Stampacchia Theorem, on variational inequalities, holds on a Banach space X, then X is isomorphic to a Hilbert space. Motivated by…
Hilbert space structure and positive operators
D. Drivaliaris, N. Yannakakis
Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits…
Generalizations of the Lax-Milgram theorem
D. Drivaliaris, N. Yannakakis
We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular we give sufficient conditions for a real-valued function defined on the product of a refl…
Subspaces with a common complement in a Banach space
D. Drivaliaris, N. Yannakakis
We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs…