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

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

ISBN-10: 3034806388

ISBN-13: 9783034806381

ISBN-10: 3034806396

ISBN-13: 9783034806398

This quantity is devoted to Leonid Lerer at the celebration of his 70th birthday. the most half offers fresh leads to Lerer’s examine niche, such as Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia sort effects, matrix polynomials, and comparable parts in operator and matrix concept. Biographical fabric and Lerer's record of courses entire the volume.

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

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1) if and only if the operator ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ???????? ???? ∗ ???? ∗ ???? ???? ⎣ ???? ????????∗ ???? ⎦ : ⎣???? ⎦ → ⎣???? ⎦ is positive semidefinite. 2) ???? ????∗ ???????? ???? ???? On the other hand, if ????????∗ ≥ ???????? ∗ , then there exist (unique) contractions ????1 ∈ ℒ(????, Ran????) and ????2 ∈ ℒ(????, Ran????) such that 1 (????????∗ ) 2 ????1 = ????, 1 (????????∗ ) 2 ????2 = ????, Ker????1 = Ker????, Ker????2 = Ker????. , [6] for the proof). 1. Let ????????∗ ≥ ???????? ∗ . 3) and where the parameter ???? is an arbitrary contraction from Ran(???? − ????1∗ ????1 ) into Ran(???? − ????2∗ ????2 ).

His teaching manner was calm and pleasing. His explanations always were very clear and accurate. Atmosphere he created was always good and friendly. The subject of my research was chosen. It was related to factorizations of column and row reduced matrix polynomials. At the beginning our meetings were not so frequent, later on we met much more often. But every meeting was very useful and productive for me. Sometimes my research progress was good and smooth, sometimes I felt frustrated from unsuccessful attempts to find a solution of some 12 I.

13). 13). 6, this condition in turn is equivalent to □ positivity of the kernel ???????? (????, ????) on ???? × ????. 1 can be written in the form ????????∗ ???? ???? = x. 5 apply leading us to the following result. 4. 5) respectively. 1 1. 1 (i) has a solution if and only if x ∈ Ran ????????2 . 2. 1 (i) and has the minimal possible norm ∥????min∥ℋ(????????,???? ) = ∥???????? 2 x∥. 3. A function ℎ ∈ ℋ(????????,???? ) satisfies (???? ∗ ℎ)∧???? (???? ∗ ) = 0 if and only if ℎ is in the ˜ ????,???? ) with reproducing kernel reproducing kernel Hilbert space ℋ(???? ∗ ˜ ????,???? (????, ????) = ???????? − ????(????)????(????) − ???? ???? (????)???? −1 ???? ???? (????)∗ .

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Advances in Structured Operator Theory and Related Areas: The Leonid Lerer Anniversary Volume by M. A. Kaashoek (auth.), Marinus A. Kaashoek, Leiba Rodman, Hugo J. Woerdeman (eds.)

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