Advances in Structured Operator Theory and Related Areas: by M. A. Kaashoek (auth.), Marinus A. Kaashoek, Leiba Rodman,

By M. A. Kaashoek (auth.), Marinus A. Kaashoek, Leiba Rodman, Hugo J. Woerdeman (eds.)

This quantity is devoted to Leonid Lerer at the get together of his 70th birthday. the most half provides contemporary ends up in Lerer’s learn niche, including Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia style effects, matrix polynomials, and comparable components in operator and matrix thought. Biographical fabric and Lerer's checklist of guides whole the volume.

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Extra info for Advances in Structured Operator Theory and Related Areas: The Leonid Lerer Anniversary Volume

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1) = (???? + ???? − 1)! 1) that the spaces ????1 (????) and ????2 (????) are respectively the standard vector-valued Hardy space ???? 2 (????) and the unweighted Bergman space ????22 (????) of the unit disk. It then follows that ???????? (????) is the reproducing kernel Hilbert space with reproducing kernel 1 ???????? (????, ????) = ???????? (1 − ????????)???? and that for ???? > 1, the ???????? (????)-norm equals ∫ 2 ∥???? ∥????????(????) = (???? − 1) ∥???? (????)∥2???? (1 − ∣????∣2 )????−2 ????????(????) < ∞ ???? where ???????? is the planar Lebesgue measure normalized so that ????(????) = 1.

1. 3), we now introduce ℒ(???? , ????)-valued functions ???????????? (????) = (???? − ????(????)???? )(???? − ???????? )−???? , ???? = 1, . . 11) which are therefore completely specified by the data set (????, ????, ????, ????(????), x). 10). 3. 5) respectively. Then Interpolation in Sub-Bergman Spaces 27 1. 11) is in the space of multipliers ℳ(???? , ℋ(????????,???? )), and moreover [∗] ???????? ???? ???????????????? = ???????? ???? [ and [∗] ∗ ???????? ???? = ????????,????,???? . 13) ???? ] ???????? ???????????? (????)∗ is positive on ???? × ????. 2. The kernel ???????? (????, ????) = ???????????? (????) ????????,???? (????, ????) Proof.

8]) that the operator ???? is strongly stable in the sense that ???? ???? converge to zero in the strong operator topology. 15) 0 −???????? ????(????) ????(????) be a ℒ(???? ⊕ ????)-valued function such that for all ????, ???? ∈ ????, [ ] [ ???? − Θ(????)????Θ(????)∗ ???? = (???? − ???????? )−1 ????1−1 (???? − ???????? ∗ )−1 ???? ∗ ???? 1 − ???????? ] ????∗ . 16) uniquely up to a constant ????unitary factor on the right. 16) is [ ] ???? Θ(????) = ???? + ???? (???? − ???????? )−1 ???? ???? [ ???? ] ???? ] : ???? ⊕???? → where the operator [ ???? ????⊕???? is an injective solution to the ????-Cholesky factorization problem ⎡ ⎤ ] [ −1 [ ] ???? ] [ ] [ ???? 0 ???? − ⎣ ???? ⎦ ????1−1 ???? ∗ ???? ∗ ???? ∗ .

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