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Noah Schweber
Noah Schweber
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Let A be the infinite Hankel matrix with the coefficient A_{kj}=exp(-t(k+j)^2)-exp(-t(k+j+2)^2),$$A_{kj}=e^{(-t(k+j)^2)}-e^{(-t(k+j+2)^2)},$$ with t$t$ a nonnegative real number.

Is A in$A$ in trace class with a norm bounded by an absolute constant?

It is not hard to see A is in trace class with a constant depending on t by either a result of J. S. Howland (MR0288630) or V. Peller (MR0602274). But the mystery is wether we can get rid of t?

Let A be the infinite Hankel matrix with the coefficient A_{kj}=exp(-t(k+j)^2)-exp(-t(k+j+2)^2), with t a nonnegative real number.

Is A in trace class with a norm bounded by an absolute constant?

It is not hard to see A is in trace class with a constant depending on t by either a result of J. S. Howland (MR0288630) or V. Peller (MR0602274). But the mystery is wether we can get rid of t?

Let A be the infinite Hankel matrix with the coefficient $$A_{kj}=e^{(-t(k+j)^2)}-e^{(-t(k+j+2)^2)},$$ with $t$ a nonnegative real number.

Is $A$ in trace class with a norm bounded by an absolute constant?

It is not hard to see A is in trace class with a constant depending on t by either a result of J. S. Howland (MR0288630) or V. Peller (MR0602274). But the mystery is wether we can get rid of t?

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tao mei
tao mei
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Is this Hankel matrix in trace class

Let A be the infinite Hankel matrix with the coefficient A_{kj}=exp(-t(k+j)^2)-exp(-t(k+j+2)^2), with t a nonnegative real number.

Is A in trace class with a norm bounded by an absolute constant?

It is not hard to see A is in trace class with a constant depending on t by either a result of J. S. Howland (MR0288630) or V. Peller (MR0602274). But the mystery is wether we can get rid of t?