Abstract: A contraction T (that is, an operator with ||T|| ≤ 1) on a Hilbert space H is said to be pure if the sequence T^{*n} converges to 0 in the strong operator topology. The fundamental analytic model of Sz.–Nagy–Foias shows that these contractions are unitarily equivalent to certain compressions of the shift operator on some Hilbert space. This outcome arises from an important result: a pure contraction always dilates to a pure isometry.

In this talk, we will initiate our exploration by addressing the question: can a pair of commuting pure contractions dilate to pure isometries? We will identify certain pairs of commuting contractions that affirmatively answer this question. Generally, pure contractive Toeplitz operators on Hilbert spaces of analytic functions play a vital role in connecting diverse fields such as operator theory and several complex variables. Despite this significance, a comprehensive understanding has been lacking regarding the conditions under which a Toeplitz operator transforms into a pure contraction. In the second segment of the presentation, we will provide answers to this question for analytic Toeplitz operators acting on well-known Hilbert spaces of analytic functions.

Meeting id: 948 0044 7244
Passcode: 597063