# Analysis Seminar 2005-06

**Wednesday** September 7th, 2005 2.30pm TCD E. Effros (UCLA & HMI) Some remarkable Hopf 2.6 algebras that arise in non-commutative functional analysis 4.00 TCD G. Murphy (UCC) Noncommutative 2.6 geometry, quantum symmetries and quantum dimension Tuesday September 13th, 2005 3.00pm UCD E. Effros (UCLA & HMI) Some remarkable Hopf Maths Sem algebras that arise in non-commutative functional analysis, II Tuesday September 20th, 2005 12.00 TCD E. Effros (UCLA & HMI) Recent developments in 2.6 operator space theory 2.30pm TCD M. Mathieu (QUB) Answering a question of 2.6 G K Pedersen 4.00 TCD S. Wills (UCC) Operator cocycles on 2.6 Fock space Tuesday October 4th 3.00pm UCD R. Harte A Taylor spectrum for Maths Sem algebras? 4.20 UCD M. Venkova Fredholm operators Maths Sem depending on a parameter (Note unusual day) Friday, October 14 3.00pm UCD L. Harris (Kentucky) Derivative estimates for Maths Sem polynomials on Banach spaces 4.20 UCD C. Earle (Cornell & A dynamical approach to Maths Sem Warwick) barycentric extension

**Abstract** for L. Harris: We begin with a discussion of inequalities
between norms of multilinear mappings and homogeneous polynomials
on various spaces. We then turn to analogues of the inequalities
of Bernstein and Markov. Several open problems will be discussed.

**Abstract** for C. Earle: Unless it assigns measure 1/2 to two distinct points,
every probability measure on the unit circle has a well defined "conformal
barycenter" in the closed unit disk. Abikoff gave an iterative procedure -
based on a generalization of the Denjoy-Woolf theorem - for computing it.

We shall explain that procedure and how it is used in joint work with Abikoff and Mitra both to give a new definition of the barycenter and to extend self-maps of the unit circle to self-maps of the closed unit disc, generalizing previous work of Douady and Earle.

Tuesday, October 18 4.00pm TCD L. Harris (Kentucky) Fixed points of Holomor- 2.6 phic Mappings on a Banach Space

**Abstract:** This talk gives a basic introduction to infinite dimensional
holomorphic functions and associated fixed point theorems. The
numerical range of holomorphic functions is introduced and conditions
on it are given for the existence of fixed points. These results
are applied to give a quantitative version of the inverse function
theorem.

Tuesday October 25th, 2005 4.00pm UCD C. Boyd Determining the isometry Maths Sem group of weighted spaces of holomorphic functions There will also be an organisational meeting for the term's seminars. Tuesday November 1 3.00pm TCD B. Yan Singular boundary value 2.6 problems for second order differential equations 4.20 TCD D. Zaitsev Smooth CR manifolds 2.6 with exotic automorphism groups Tuesday November 8 3.30pm UCD S. Dineen Generalised inverses of Maths Sem Fredholm operators 5.15 UCD R. Timoney A result of Cabrelli and Maths Sem Molter on wavelet frames Tuesday November 15 3.00pm TCD M. Mackey Horizontal chords 2.6 Tuesday November 22 3.30pm UCD I. Short (NUIM) Quaternions, continued Maths Sem fractions and hyperbolic geometry 4.45 UCD B. Grecu (U. Valencia) Symmetric tensors of Maths Sem unit norm Tuesday November 29 3.00pm TCD C. Radu The maximal tensor 2.6 norm on operator spaces 4.20 TCD D. Kitson Hilbert modules over 2.6 function algebras Tuesday January 17th, 2006 3.30pm TCD C. O Dunlaing Barycentric mappings 2.6 Tuesday January 24th 3.30pm UCD C. O Dunlaing Barycentric mappings, II Maths Sem 4.45 UCD R. Harte A connection with Hopf Maths Sem algebras Tuesday January 31st, 2006 3.00pm TCD R. Timoney Schur multipliers 2.6 Tuesday February 7th 3.30pm UCD C. Boyd Isometry groups for Maths Sem weighted spaces of holomorphic functions 4.45 UCD R. Hügli Geometry of tripotents Maths Sem Tuesday February 14th, 2006 4.00pm UCD R. Hugli Quaternion symmetric Maths Sem spaces and the laws of Physics Tuesday February 21st 3.00pm UCD J. Loan (NUIG) Tensor products of Maths Sem Banach Lattices 4.20 UCD M. Venkova Holomorphically Maths Sem complemented famlies of subspaces of a Banach space Tuesday February 28th 3.00pm TCD R. Timoney The central Haagerup 2.6 tensor product 4.20 TCD D. Zaitsev On the Chern-Moser 2.6 normal form Tuesday March 7th 3.00pm UCD R. Timoney The central Haagerup Maths Sem tensor product, II 4.20 UCD M. Venkova Holomorphically Maths Sem complemented famlies of subspaces of a Banach space Tuesday April 11th, 2006 3.00pm UCD I. Zalduendo Orthogonally additive Maths Sem (Universidad Torcuato polynomials over C(K) de Tella, Buenos Aires) 4.20pm UCD S. Dineen Relative Inverses Maths Sem Tuesday April 18th, 2006 3.00pm UCD R.E. Harte Residue quotients Maths Sem 4.20pm UCD R. Hugli Manifolds of tripotents Maths Sem Tuesday May 2 3.00pm UCD C. Boyd Two applications of Maths Sem Weyl's lemma 4.20 UCD S. Dineen Generalised inverses Maths Sem Tuesday May 9 3.00pm TCD L. Nilsson Kergin operators 2.6 4.20 TCD M. Mackey Essentially isolated 2.6 composition operators Tuesday June 13 3.00pm TCD V. Paulsen (Houston) Schur products and 2.6 MASA bimodule projections, I 4.20 TCD V. Paulsen (Houston) Schur products and 2.6 MASA bimodule projections, II Friday June 16 4.00pm UCD M. Klimek (Uppsala) Block frames in Hilbert Sem spaces and stochastic flows