Advances in Invariant Subspaces and Other Results of Operator Theory

Some topics in the theory of decomposable operators.- Korovkin closures in Banach algebras.- On the theory of the class % MathType!MTEF!2!1!+-% feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa% aaleaacqGH1ecWdaWgaaadbaGaaGimaaqabaaaleqaaaaa!397A!$${A_{{aleph _0}}}$$ with applications to invariant subspaces and the Bergman shift operator.- Examples of chains of invariant subspaces.- Isometric dilations of commuting contractions. IV.- Recent results on reflexivity of operators and algebras of operators.- Schur analysis for matrices with finite number of negative squares.- Uniform algebras, Hankel operators and invariant subspaces.- Contractions génériques.- Hilbert modules over function algebras.- Differential equation of an inner function. II.- On a class of unitary operators in Krein space.- Naimark dilations, state-space generators and transmission lines.- Contractions being weakly similar to unitaries.- A characterization of generalized zeros of negative type of functions of the class N?.- Skew-symmetric operators and isometries on a real Banach space with a hyperorthogonal basis.- On the operator equation ax + (ax)* ? ?x= b.- On the inverse problem of a dissipative scattering theory. I.- Some spectral properties of an operator.- Hyponormal operators and eigendistributions.- The invariant subspace problem: a description with further applications of a combinatorial proof.- Some results on cohomology with Borel cochains, with applications to group action on operator algebras.- Spectral mapping theorems for analytic functionalcalculi.- Prediction theory and choice sequences: an alternate approach.- Idael properties of order bounded operators on ordered Banach spaces which are not Banach lattices.- More about pseudodifferential operators on bounded domains.