Related papers: Nonlinear subsets of function spaces and spaceabil…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

We derive new results about existence and uniqueness of local and global solutions for nonlinear Schrodinger equation, including self-similar global solutions. Our analysis is performed in the framework of Marcinkiewicz spaces.

Using a nonlinear version of the well known Hardy-Littlewood inequalities, we derive new formulas for decreasing rearrangements of functions and sequences in the context of convex functions. We use these formulas for deducing several…

We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…

We prove in this article the well posedness of non - linear Ordinary Differential Equations (ODE) of first and second order in Orlicz spaces with unbounded domain of definition.

For each $n \in \mathbb{N}$ a Banach space $\mathfrak{X}_{0,1}^n$ is constructed is having the property that every normalized weakly null sequence generates either a $c_0$ or $\ell_1$ spreading models and every infinite dimensional subspace…

In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locally-finite weights on a semi-finite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz…

We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of…

Certain solvable extensions of $H$-type groups provide noncompact counterexamples to the so-called Lichnerowicz conjecture, which asserted that ``harmonic'' Riemannian spaces must be rank 1 symmetric spaces.

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a…

We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…

It is introduced an open class of linear operators on Banach and Hilbert spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace. In certain cases, the non-wandering set coincides with the whole…

Given a map $f \colon E \longrightarrow F$ between Banach spaces (or Banach lattices), a set $A$ of $E$-valued bounded sequences, ${\bf x} \in A$ and a vector topology $\tau$ on $F$, we investigate the existence of an infinite dimensional…

The theorem on the existence of maximal nonnegative invariant subspaces for a special class of dissipative operators in Hilbert space with indefinite inner product is proved in the paper. It is shown in addition that the spectra of the…

In this short note we prove the result stated in the title; that is, for every $p>0$ there exists an infinite dimensional closed linear subspace of $L_{p}[0,1]$ every nonzero element of which does not belong to $\bigcup\limits_{q>p}…

In this article we investigate the Fourier series and transforms for the functions defined on the $ [0, 2 \pi]^ d $ or $ R^d $ and belonging to the exponential Orlicz and some other rearrangement invariant (r.i.) spaces.

If T is a bounded linear operator acting on an infinite-dimensional Banach space, then there exists and operator F of rank at most one and arbitrarily small norm such that T-F has an invariant subspace of infinite dimension and codimension.…

In this paper, equivalence between interpolation properties of linear operators and monotonicity conditions are studied, for a pair $(X_0,X_1)$ of rearrangement invariant quasi Banach spaces, when the extreme spaces of the interpolation are…