Cyclic Vectors of Lambert's Weighted Shifts

B. S. Yadav, S. Chatterjee
1980 Proceedings of the American Mathematical Society  
Let B(H) denote the Banach algebra of all bounded linear operators on an infinite-dimensional separable complex Hubert space H, and let I2 be the Hilbert space of all square-summable complex sequences x = {*", xx, x2,... }. For an injective operator A in B(H) and a nonzero vector / in H, put wm = \\Amf\\/\\Am-xf\\, m = 1, 2, .... The operator TAJ on I2, defined by TA/x) = [wxxx, w2x2,. . . }, is called a weighted (backward) shift with the weight sequence {wm}m-i-This paper is concerned with the
more » ... investigation of the existence of cyclic vectors of TAJ. Also it is shown that if A satisfies certain nice conditions, then every transitive subalgebra of B(H) containing TAJ coincides with B(H).
doi:10.2307/2042153 fatcat:pbfwzc62crgp7fqksmwmzdjevq