Curvature and the backward shift operators
نویسندگان
چکیده
منابع مشابه
Hypercyclic Operators That Commute with the Bergman Backward Shift
The backward shift B on the Bergman space of the unit disc is known to be hypercyclic (meaning: it has a dense orbit). Here we ask: “Which operators that commute with B inherit its hypercyclicity?” We show that the problem reduces to the study of operators of the form φ(B) where φ is a holomorphic self-map of the unit disc that multiplies the Dirichlet space into itself, and that the question o...
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متن کاملPseudocontinuations and the Backward Shift
In this paper, we will examine the backward shift operator Lf = (f − f(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of “pseudocontinuation” of functions across the...
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z on the classical Hardy space H. Though there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds E ⊂ H for which BE ⊂ E . When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation deve...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1984
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1984-0735574-5