Generalizing normality for operators on Banach spaces: Hyponormality. I.
Generators for algebras dense in -spaces
For various -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...
Geometric properties of composition operators belonging to Schatten classes.
Geometry of oblique projections
Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections determined by the different involutions induced by positive invertible elements a ∈ A. The maps sending p to the unique with the same range as p and sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q,r ∈ A with ||q-r|| < 1 such that...
Gleason measures and some inner products on the algebra of bounded operators on a Hilbert space
Global existence for a Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.
Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase
In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...
Grenzordnungen von Operatorenidealen (I).
Grothendieck Numbers and Volume Ratios of Operators on Banach Spaces.
Grothendieck-Lidskiĭ theorem for subspaces of quotients of -spaces
Generalizing A. Grothendieck’s (1955) and V. B. Lidskiĭ’s (1959) trace formulas, we have shown in a recent paper that for p ∈ [1,∞] and s ∈ (0,1] with 1/s = 1 + |1/2-1/p| and for every s-nuclear operator T in every subspace of any -space the trace of T is well defined and equals the sum of all eigenvalues of T. Now, we obtain the analogous results for subspaces of quotients (equivalently: for quotients of subspaces) of -spaces.
Growth of (frequently) hypercyclic functions for differential operators
We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions for these functions on particular rays or sectors. Our research extends known results in several respects.
Growth of operator valued meromorphic functions.
Gruppen und Halbgruppen verallgemeinerter Skalaroperatoren.