By Radu Gadidov (auth.), Raúl E. Curto, Palle E. T. Jørgensen (eds.)

The concept of operators stands on the intersection of the frontiers of recent research and its classical opposite numbers; of algebra and quantum mechanics; of spectral conception and partial differential equations; of the trendy worldwide method of topology and geometry; of illustration idea and harmonic research; and of dynamical structures and mathematical physics. the current choice of papers represents contributions to a convention, they usually were conscientiously chosen with a purpose to bridging diverse yet similar parts of arithmetic that have only in the near past displayed an unforeseen community of interconnections, in addition to new and intriguing cross-fertilizations. Our unify ing subject is the algebraic view and method of the learn of operators and their purposes. The complementarity among the variety of issues at the one hand and the cohesion of principles at the different has been under pressure. a number of the longer contributions characterize fabric from lectures (in elevated shape and with proofs for the main part). notwithstanding, the shorter papers, in addition to the longer ones, are a vital part of the image; they've got all been conscientiously refereed and revised that allows you to a team spirit of goal, timeliness, clarity, and vast attraction. Raul Curto and Paile E. T.

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Hence, if T = T*, then T is real-valued on L\(A) and thus u(T) ~ R whenever T has natural spectrum. Consequently, the symmetry of A implies that B := M6(A) is symmetric. By the Stone-Weierstrass theorem, Ii is dense in C(L\(B», which implies that the Choquet boundary and hence the Shilov boundary of B is the whole of L\(B). ,p E L\(M(A», cf. 3 of (22). ,p2 on L\(B). In particular, if A is a semi-simple commutative Banach *-algebra which is both regular and symmetric and has a bounded approximate identity, then the preceding results show that D(A) is a full and symmetric closed *-subalgebra of M(A) whose spectrum is a quotient of L\(M(G}).

T E £(1i)n with ~¥) ~ 0, ~) ~ 0 an appropriate extension to several variables of the class of contractions? Problem 2. State and prove a commutant lifting theorem for the above class. Problem 3. Prove a Wold type decomposition for spherical isometries. Problem 4. ). , Hypercontractions and subnormality, J. Operator Theory 13(1985), 203-217. , On the intertwining of joint isometries, J. Operator Theory 23(1990), 339--350. , Model theory on the unit ball in Theory (to appear). [CuVa] Curto, R. E.

However, the approach might be tedious. Is there a different approach to the questions? We don't know the answer to this. Erdos and Power [10] have successfully classify all bimodules of nest algebras which are closed in the strong operator topology. They proved that each strong closed bimodule is singly generated under the strong topology. In a conversation, Arveson suggested to the author the following question. Question 3 Classify the norm-closed bimodules of nest algebras. Questions on bimodules of nest algebras 55 This question is open even in B(1i) case.