SUPERCYCLICITY OF JOINT ISOMETRIES
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Let H be a separable complex Hilbert space. A commuting tuple T = (T1, . . . , Tn) of bounded linear operators on H is called a spherical isometry if ∑n i=1 Ti*Ti = I. The tuple T is called a toral isometry if each Ti is an isometry. In this paper, we show that for each n ≥ 1 there is a supercyclic n-tuple of spherical isometries on Cn and there is no spherical or toral isometric tuple of operators on an infinite-dimensional Hilbert space.
Abstract
Let H be a separable complex Hilbert space. A commuting tuple T = (T1, . . . , Tn) of bounded linear operators on H is called a spherical isometry if ∑n i=1 Ti*Ti = I. The tuple T is called a toral isometry if each Ti is an isometry. In this paper, we show that for each n ≥ 1 there is a supercyclic n-tuple of spherical isometries on Cn and there is no spherical or toral isometric tuple of operators on an infinite-dimensional Hilbert space.
참고문헌 (7)
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