21 documents found, page 1 of 3
A note on the essential numerical range of block diagonal operators
Carvalho, L.; Diogo, C.; Mendes, S.; Soares, H.In this note, we characterize the essential numerical range of a block diagonal operator T = ?i Ti in terms of the numerical ranges {W(Ti)}i of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of {W(Ti)}i. This characterization can be simplified further. In fact, we prove the existence of a decomposition of T for which the convex hull is not required.
On the convexity of the quaternionic essential numerical range
Carvalho, L.; Diogo, C.; Mendes, S.; Soares, H.The numerical range in the quaternionic setting is, in general, a non-convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense, infinite multiplicity. We prove that the essential numerical range of a bounded linear operator on a quaternionic Hilbert space is convex. A quaternionic analogue of Lancaster theor...
Quaternionic essential numerical range of complex operators
Carvalho, L.; Diogo, C.; Mendes, S.; Soares, H.We study the essential numerical range of complex operators on a quaternionic Hilbert space and its relation with the essential S-spectrum. We give a new characterization of the essential numerical range relating it to the complex essential numerical range. Moreover, we show that the quaternionic essential numerical range of a normal operator is the convex hull of the essential S-spectrum.
Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
Mendes, S.; Soares, H.; Miró-Roig, M.We find the complete integer solutions of the equation X2 + Y2 + Z2 − 4XY − 4YZ + 10XZ = 1. As an application, we prove that, for each solution (a, b, c) such that a > 0, b − 2a > 0 and (b − 2a)2 ≥ 4a, there is a vector bundle E on ℙ3 defined by a minimal linear resolution 0 → Oℙ3 (−2)a → Oℙ3 (−1)b → Oℙc3 → E → 0. In particular, E satisfies ?(End E) = 1.
A family of vector bundles on P3 of homological dimension 2 and X (EndE) = 1
Soares, H.; Miró-Roig, M.; Mendes, S.For any odd integer ? ≤ −5, we construct a family of rank 3 vector bundles {E? } on P3 with minimal linear resolution and satisfying ? (End E? ) = 1.
A family of vector bundles on P3 of homological dimension 2 and X (EndE) = 1
Soares, H.; Miró-Roig, M.; Mendes, S.For any odd integer ? ≤ −5, we construct a family of rank 3 vector bundles {E? } on P3 with minimal linear resolution and satisfying ? (End E? ) = 1.
A family of vector bundles on P3 of homological dimension 2 and X (EndE) = 1
Soares, H.; Miró-Roig, M.; Mendes, S.For any odd integer ? ≤ −5, we construct a family of rank 3 vector bundles {E? } on P3 with minimal linear resolution and satisfying ? (End E? ) = 1.
A family of vector bundles on P3 of homological dimension 2 and X (EndE) = 1
Soares, H.; Miró-Roig, M.; Mendes, S.For any odd integer ? ≤ −5, we construct a family of rank 3 vector bundles {E? } on P3 with minimal linear resolution and satisfying ? (End E? ) = 1.
Social infrastructure and the preservation of physical capital: equilibria and ...
Soares, H.; Sequeira, T. N.; Marques, P. M.; Gomes, O.; Ferreira-Lopes, A.We study the mechanisms according to which social infrastructure influences the preservation of physical capital and, consequently, economic growth. The model considers that social infrastructure is a specific type of human capital, which acts in order to preserve already existing physical capital, by, e.g., reducing the incentive for rent seeking or corruption. Using an innovative methodology in economics, the...
Monads on projective varieties
Marchesi, S.; Marques, P. M.; Soares, H.We generalize Floystad's theorem on the existence of monads on projective space to a larger set of projective varieties. We consider a variety X, a line bundle L on X, and a basepoint-free linear system of sections of L giving a morphism to projective space whose image is either arithmetically Cohen-Macaulay (ACM) or linearly normal and not contained in a quadric. We give necessary and sufficient conditions on ...