Toeplitz operators associated to commuting row contractions

Let H be a complex Hilbert space and let {Tn}_n?1 be a sequence of commuting bounded operators on H such that . Let denote the space of all operators X in B(H) for which and suppose that . We will show that there exists a triple {K,Γ,{Un}_n?1} where K is a Hilbert space, Γ:K→H is a bounded operator and {Un}_n?1⊂B(K) is a sequence of commuting normal operators with such that TnΓ=ΓUn for n?1, and for which the mapping Y?ΓYΓ^∗ is a complete isometry from the commutant of {Un}_n?1 onto the space . Moreover we show that the inverse of this mapping can be extended to a ^∗-homomorphism

     

A new flavonoid and sulphur-containing amides from Glycosmis chlorosperma

A new flavonoid, dihydroglychalcone-A, was isolated from the leaves extract of Glycosmis chlorosperma in addition to two known sulphur-containing amides, dambullin and gerambullin. The structure of the new compound was assigned as 2'-hydroxy-4,6'-dimethoxy-3',4'-(2",2"-dimethylpyrano)dihydrochalcone. The extract of the leaves was also found to exhibit antimicrobial and cytotoxic activities.     

Invariant subspaces and localizable spectrum

LetT L(X) be a continuous linear operator on a complex Banach spaceX. We show thatT possesses non-trivial closed invariant subspaces if its localizable spectrum _loc(T) is thick in the sense of the Scott Brown theory. Since for quotients of decomposable operators the spectrum and the localizable spectrum coincide, it follows that each quasiaffine transformation of a Banach-space operator with Bishop's property () and thick spectrum has a non-trivial invariant subspace. In particular it follows that invariant-subspace results previously known for restrictions and quotients of decomposable operators are preserved under quasisimilarity.     

Some exact sequences for Toeplitz algebras of spherical isometries

A family of commuting bounded operators on a Hilbert space is said to be a spherical isometry if in the weak operator topology. We show that every commuting family of spherical isometries is jointly subnormal, which means that it has a commuting normal extension on some Hilbert space Suppose now that the normal extension is minimal. Then we show that every bounded operator in the commutant of has a unique norm preserving extension to an operator in the commutant of Moreover, if is the commutator ideal in then is *-isomorphic to We also show that the commutant of the minimal normal extension is completely isometric, via the compression mapping, to the space of Toeplitz-type operators associated to We apply these results to construct exact sequences for Toeplitz algebras on generalized Hardy spaces associated to strictly pseudoconvex domains.

     

A Poisson boundary for topological semigroups

We give a non-probabilistic proof for the boundary integral representation of μ-harmonic functions on topological semigroups.     

On the commutant of hyponormal operators

Let be a pure hyponormal operator with compact self-commutator. We show that the unit ball of the commutant of is compact in the strong operator topology.

     

Invariant subspaces for polynomially hyponormal operators

We show that if is a bounded operator on a Hilbert space such that for every polynomial , then has a nontrivial invariant subspace.

     

Estimation of Free Radical Polymerization Rate Coefficients Using Computational Chemistry

This study explores the application of computational chemistry to estimate free radical polymerization rate coefficients. The Evans-Polanyi relationship is combined with computed heats of polymerization to estimate copolymerization reactivity ratios for many vinyl monomer pairs, focusing on acrylates, methacrylates and styrene, with accuracy assessed by comparison to experimental values. The effect of different optimization approaches on the values of thermodynamic properties is explored, and it is concluded that a combination of conventional optimization and relaxed potential energy scans was most effective at identifying global minima. The difference between thermodynamic properties calculated using the harmonic oscillator treatment and a hindered rotor model is evaluated for methyl methacrylate polymerization.