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

This quantity is devoted to Leonid Lerer at the party of his 70th birthday. the most half offers fresh ends up in Lerer’s study niche, together with Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia kind effects, matrix polynomials, and similar components in operator and matrix idea. Biographical fabric and Lerer's checklist of guides entire 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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19) Interpolation in Sub-Bergman Spaces 29 mapping the Schur class ????(????, ????) into itself. 19) establishes a one-to-one correspondence between ????(????, ????) and the set of all Schur class functions ???? such that (???? ∗ ????)∧???? (???? ∗ ) = ???? ∗ . 3) of ???? , it follows that ???? = TΘ [ℰ] for some (uniquely determined) function ℰ ∈ ????(????, ????) which is recovered from ???? by ℰ = (???? − ????????)−1 (???????? − ????). 20) Since Θ is ????-inner, it follows that ????(????) is boundedly invertible for all ???? ∈ ???? and also ∥????−1 (????)????(????)∥ < 1 for all ???? ∈ ????.

Fortunately, I could return to Haifa for several more Haifa Matrix Meetings and an ILAS Meeting over the course of the years, most of them combined with some extra time to work together with Leonia. I would like to close with a heartfelt thanks to Leonia for his inspiring lead in our joint work and for his warm friendship. M. nl Operator Theory: Advances and Applications, Vol. 237, 15–15 c 2013 Springer Basel ⃝ My First Research Experience Hugo J. Woerdeman My first exposure to mathematical research was under the supervision of Professor Leonid (“Leonia”) Lerer during the academic year 1984–1985.

Indeed, let us first note that ( )−1 ???? − (???? − ????)???? (???? − ???????? )−1 ????1−1 (???????? − ???? ∗ )−1 ???? ∗ )−1 ( = ???? + (???? − ????) ???? − (???? − ????)???? (???? − ???????? )−1????1−1 (???????? − ???? ∗ )−1 ???? ∗ × ???? (???? − ???????? )−1 ????1−1 (???????? − ???? ∗ )−1 ???? ∗ ( )−1 = ???? + (???? − ????)???? ???? − (???? − ????)(???? − ???????? )−1????1−1 (???????? − ???? ∗ )−1 ???? ∗ ???? × (???? − ???????? )−1 ????1−1 (???????? − ???? ∗ )−1 ???? ∗ = ???? + (???? − ????)???? Δ(????)−1 ???? ∗ . With this result in hand we see next that )−1 ( ????(????)−1 ????(????) = (???? − ????) ???? − (???? − ????)???? (???? − ???????? )−1 ????1−1 (???????? − ???? ∗ )−1 ???? ∗ × ???? (???? − ???????? )−1 ????1−1 (???????? − ???? ∗ )−1 ???? ∗ ) ( = (???? − ????) ???? + (???? − ????)???? Δ(????)−1 ???? ∗ × ???? (???? − ???????? )−1 ????1−1 (???????? − ???? ∗ )−1 ???? ∗ = (???? − ????)???? Δ(????)−1 (Δ(????) + (???? − ????)???? ∗ ???? ) × (???? − ???????? )−1????1−1 (???????? − ???? ∗ )−1 ???? ∗ = (???? − ????)???? Δ(????)−1 ???? ∗ .

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