Analytic extensions of the metaplectic representation by integral operators of Gaussian type have been calculated in the and the Bargmann-Fock realisations by Howe [How2] and Brunet-Kramer [Brunet-Kramer, Reports on Math. Phys., 17 (1980), 205-215]], respectively. In this paper we show that the resulting semigroups of operators are isomorphic and calculate the intertwining operator.
Let be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of , the algebra of all bounded linear operators on a Hilbert space , is an automorphism.
On a compact metric space X one defines a transition system to be a lower semicontinuous map . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated.
Denote by the commutator of two bounded operators and acting on a locally convex topological vector space. If , we show that is a quasinilpotent operator and we prove that if is a compact operator, then is a Riesz operator.
In this paper we characterize those bounded linear transformations carrying into the space of bounded continuous functions on , for which the convolution identity holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.
In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator on a Hilbert space with a single spectrum satisfies