K-spectral sets and intersections of disks of the Riemann sphere

@misc{citeulike:2064556, abstract = {We prove that if two closed disks X\_1 and X\_2 of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then the intersection X\_1\cap X\_2 is a complete (2+2/\sqrt{3})-spectral set for A. When the intersection of X\_1 and X\_2 is an annulus, this result gives a positive answer to a question of A.L. Shields (1974).}, author = {Badea, Catalin and Beckermann, Bernhard and Crouzeix, Michel }, citeulike-article-id = {2064556}, eprint = {0712.0522}, keywords = {arxived, func-calc, spectral, \_unread}, month = {Dec}, posted-at = {2007-12-06 00:36:26}, priority = {4}, title = {K-spectral sets and intersections of disks of the Riemann sphere}, url = {http://arxiv.org/abs/0712.0522}, year = {2007} }

TY - ELEC ID - citeulike:2064556 L3 - citeulike-article-id:2064556 TI - K-spectral sets and intersections of disks of the Riemann sphere N2 - We prove that if two closed disks X_1 and X_2 of the Riemann sphere are spectral sets for a bounded linear operator A on a Hilbert space, then the intersection X_1\cap X_2 is a complete (2+2/\sqrt{3})-spectral set for A. When the intersection of X_1 and X_2 is an annulus, this result gives a positive answer to a question of A.L. Shields (1974). KW - arxived KW - func-calc KW - spectral KW - _unread AU - Badea, Catalin AU - Beckermann, Bernhard AU - Crouzeix, Michel PY - 2007/Dec/04/ UR - http://arxiv.org/abs/0712.0522 ER -