Operator techniques in functional analysis, complex analysis,
and stochastic processes
Grant No. 2-CEx06-11-34/25.07.2006
October 2006 - November 2008
Short description of the research project
The research area represents a hot domain of international
research,
with important implications in practical problems. The project intends to
capitalize on the vast experience of the teams implied,
by applying different techniques and methods of operator theory to
problems of major interest in current research.
It is structured on four major themes of research:
1. Functional models and invariant subspaces for multioperators.
One studies the possibilities of extension of single operator theory in
Banch and Hilbert spaces to commutative familie of operators;
in particular, one intends to find models based on function spaces as well
as
to determine invariant subspaces for multioperators.
2. Differential operators and stochastic processes.
One intends to apply operator techniques to the study of
concrete operators obtinaed form partial derivtives equations and
stochastic processes; in particular, spectral analysis for differnt types
of
operators will be developed.
3. C*-algebras, von Neumann algebras and number theory.
One studies mainly the interrelation between modern theory of
operator algebras and the old traditional domain of number theory.
The results have important applications in current problems of
statistical mechanics.
4. Operator methods in function spaces and differential geometry.
One intends to apply operator methods in the study of current problems of
domains that have a classical flavour:
real analysis, functions of several complex variables, differential
geometry.
Project coordinator
- Dr. Calin Ambrozie
- Dr. Daniel Beltita
- Dr. Florin Boca
- Dr. Aurelian Gheondea
- Dr. Radu Gologan
- Dr. Marius Mantoiu
- Dr. Camil Muscalu
- Dr. Remus Nicoara
- Dr. Viorel Nitica
- Dr. Mihai Popa
- Dr. Nicolae Popa
- Dr. Ionel Popescu
- Dr. Iulian Popescu
- Dr. Bebe Prunaru
- Dr. Florin Radulescu
- Dr. Ivan Singer
- Dr. Serban Stratila
- Dr. Vlad Timofte
- Dr. Ilie Valusescu
Ph.D. students
- Raluca Dumitru
- Adrian Ioana
- Victor Lie
- Anca-Nicoleta Marcoci
- Liviu-Gabriel Marcoci
- Liviu Paunescu
- Bogdan Visinescu
Scientific coordinator
- Lect. Dr. Aurelian Craciunescu
- Lect. Dr. Pastorel Gaspar
- Dr. Laurian Suciu
- Prof. Dr. Nicolae Suciu
Ph.D. students
- Iuliana Borza
- Loredana Ciurdariu
- Nicolae Lupa
- Sorin Nadaban
Research that was financially supported in 2006 (1st phase of
the project)
- F. Boca,
An AF algebra associated with the Farey tessellation,
preprint.
- A. Craciunescu, Factorization properties of
commuting n-tuples of contractions, preprint.
- P. Gaspar and L. Ciurdariu,
Finite systems of commuting gramian isometries,
preprint.
Research that was financially supported in 2007 (2nd phase of
the project)
- C. Benhida, D. Timotin,
Poisson kernels and automorphism invariance properties
for multioperators, preprint.
- D. Gaspar, P.Gaspar, and N. Lupa,
Dilations on locally Hilbert spaces, preprint.
- A. Gheondea, A.S. Kavruk,
On Lebesgue type decompositions for operator valued
completely positive maps on $C^*$-algebras,
preprint.
- V. Lie,
The (weak-$L^2$) boundedness of the quadratic Carleson operator,
preprint.
- M. Popa,
Freeness with amalgamation, limit theorems and
S-transform in non-commutative probability spaces
of type B, preprint.
- F. Radulescu,
The von Neumann algebra of the non-residually finite
Baumslag group $\langle a,b | a b^3 a^-1 = b^2\rangle$
embeds into $R^\omega$,
preprint.
- L. Suciu, N. Suciu,
Harnak ordering for paris of commuting contractions,
preprint.
- V. Timofte,
An isomorhic characterization of $L^1$-spaces,
preprint.
Research that was financially supported in 2008 (3rd phase of
the project)
- F.P. Boca, R.N. Gologan,
On the distribution of the free path length of the Lorentz gas in a
honeycomb (I),
preprint.
- D. Gaspar, P. Gaspar,
A Hilbert module like treatment of Banach space valued stationary
processes,
preprint.
- D. Gaspar, P. Gaspar,
Positive definite locally Hilbert space operator valued kernels,
preprint.
- P. Gaspar, L. Popa,
The shift of a random distribution,
preprint.
- A. Marcoci, L. Marcoci, L.E. Persson, N. Popa,
Schur multiplier characterization of a class of infinite matrices,
preprint.
- L. Marcoci,
A new class of linear operators on $\ell^p$ and Schur multipliers for
them,
preprint.
- M. Mbekhta, L. Suciu,
Classes of operators similar to partial isometries,
preprint.
- M. Mbekhta, L. Suciu,
Generalized inverses and similarity to partial isometries,
preprint.
- R. Nicoara,
Subfactors and Hadamard matrices,
preprint.
- M. Popa,
A new proof for the multiplicative property of the boolean cumulants with
applications to operator-valued case,
preprint arXiv:0804.2109v2 [math.OA].
- M. Popa,
Multilinear function series in conditionally free probability with
amalgamation,
preprint arXiv:0704.0040v3 [math.OA].
- M. Popa, J.-C. Wang,
Multiplicative c-free convolution,
preprint arXiv:0805.0257v2 [math.OA].
- N. Popa,
Schur multipliers between Banach spaces of matrices,
preprint.
- Io. Popescu, Iu. Popescu,
Toeplitz algebras arising from actions of ${\mathbb N}^r$,
preprint.
- L. Suciu, N. Suciu,
Selection of semispectral measures for bicontractions,
preprint.
- I. Valusescu,
Some remarks on periodically correlated processes in complete correlated
actions,
preprint.