Abstract
Publisher Summary This chapter discusses some nuclear Hankel operators. The chapter establishes certain sufficient conditions for nuclearity directly in terms of the coefficient sequence {an}. The chapter estimates the nuclear norm ∥T∥1 for certain elementary Hankel operators T. As a corollary, the chapter shows that a non-negative decreasing sequence {an} is the coefficient sequence of a nuclear operator if the sequence is also convex, but can fail to be the coefficient sequence of a nuclear operator in the absence of convexity. The coefficient sequence {an} is a sequence of complex numbers, and sufficient conditions are obtained to support that it is the coefficient sequence of a nuclear Hankel operator.
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