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Functional Analysis
usually takes place each Tuesday at 10:00 in MÚ AV ČR, Žitná 25, konírnaChair: Vladimir Muller
PRI v dualu Asplundova prostoru zkonstruovane bez pomoci Simonsova lemmatu
M. Fabian
Tuesday, 11. December 2012 - 10:00
MÚ AV ČR, Žitná 25, konírna
$2times2$ Hadamard-Schur multipliers
S. Neuwirth
Besancon
Tuesday, 4. December 2012 - 10:00
MÚ AV ČR, Žitná 25, konírna
Hadamard-Schur multipliers are the matrix counterpart to Fourier
multipliers. They play an important role in noncommutative harmonic
analysis: they appear naturally in the study of approximation properties
of noncommutative groups like the free group or Lie groups.
In this elementary talk, I will describe how little is known even on
$2times2$ Schur multipliers.
multipliers. They play an important role in noncommutative harmonic
analysis: they appear naturally in the study of approximation properties
of noncommutative groups like the free group or Lie groups.
In this elementary talk, I will describe how little is known even on
$2times2$ Schur multipliers.
Construction of pathological Gateaux differentiable functions
Sebastian Lajara
Universidad de Castilla-La Mancha, Spain
Tuesday, 27. November 2012 - 10:00
MÚ AV ČR, Žitná 25, konírna
We establish a sufficient condition for a couple of Banach spaces X
and Y to ensure the existence of a bounded, Lipschitz, Gateaux
differentiable mapping between X and Y whose derivatives are all far
apart. This condition, which is formulated in terms of the behaviour
of an unconditional basic sequence in Y with respect to a
biorthogonal system in X, can be applied whenever X and Y are
classical Banach spaces, such as spaces of continuous functions on a
compact metric space, Orlicz sequence spaces or L^p spaces.
This lecture is based on a joint work with professors Robert Deville and Milen Ivanov.
and Y to ensure the existence of a bounded, Lipschitz, Gateaux
differentiable mapping between X and Y whose derivatives are all far
apart. This condition, which is formulated in terms of the behaviour
of an unconditional basic sequence in Y with respect to a
biorthogonal system in X, can be applied whenever X and Y are
classical Banach spaces, such as spaces of continuous functions on a
compact metric space, Orlicz sequence spaces or L^p spaces.
This lecture is based on a joint work with professors Robert Deville and Milen Ivanov.
Universal operators
V. Muller
Tuesday, 20. November 2012 - 10:00
MÚ AV ČR, Žitná 25, konírna
Let $H$ be an infinite-dimensional Hilbert space.
By a classical result of Caradus, every surjective operator $Tin B(H)$ with infinite-dimensional kernel is universal in the following sense: for each operator $S$ on a separable Hilbert space there exist a constant $c>0$ and a subspace $Msubset H$ invariant for $T$ such that the restriction $T|M$ is similar to $cS$.
We will discuss the connections of universal operators with the dilation theory and generalizations of the Caradus result for $n$-tuples of operators, both in commutative and non-commutative setting.
By a classical result of Caradus, every surjective operator $Tin B(H)$ with infinite-dimensional kernel is universal in the following sense: for each operator $S$ on a separable Hilbert space there exist a constant $c>0$ and a subspace $Msubset H$ invariant for $T$ such that the restriction $T|M$ is similar to $cS$.
We will discuss the connections of universal operators with the dilation theory and generalizations of the Caradus result for $n$-tuples of operators, both in commutative and non-commutative setting.