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Small ball properties for Fréchet spaces.

Leonhard Frerick, Alfredo Peris (2003)

RACSAM

We give characterizations of certain properties of continuous linear maps between Fréchet spaces, as well as topological properties on Fréchet spaces, in terms of generalizations of Behrends and Kadets small ball property.

Small functions and iterative methods

Michal Fečkan (1992)

Commentationes Mathematicae Universitatis Carolinae

Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.

Small sets and hypercyclic vectors

Frédéric Bayart, Étienne Matheron, Pierre Moreau (2008)

Commentationes Mathematicae Universitatis Carolinae

We study the ``smallness'' of the set of non-hypercyclic vectors for some classical hypercyclic operators.

Smooth bifurcation for a Signorini problem on a rectangle

Jan Eisner, Milan Kučera, Lutz Recke (2012)

Mathematica Bohemica

We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. We describe smooth branches of smooth nontrivial solutions bifurcating from the trivial solution branch in eigenvalues of the linearized problem. In particular, the contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tools of the proof...

Smooth operators for the regular representation on homogeneous spaces

Severino Melo (2000)

Studia Mathematica

A necessary and sufficient condition for a bounded operator on L 2 ( M ) , M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal ’Fourier multipliers with variable coefficients’ are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.

Smooth operators in the commutant of a contraction

Pascale Vitse (2003)

Studia Mathematica

For a completely non-unitary contraction T, some necessary (and, in certain cases, sufficient) conditions are found for the range of the H calculus, H ( T ) , and the commutant, T’, to contain non-zero compact operators, and for the finite rank operators of T’ to be dense in the set of compact operators of T’. A sufficient condition is given for T’ to contain non-zero operators from the Schatten-von Neumann classes S p .

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