### Citations

151 | The commutant lifting approach to interpolation problems, Operator Theory - Foias, Frazho - 1990 |

123 | An Introduction to Hilbert Space. - Young - 1997 |

105 |
Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem.
- ADAMJAN, AROV, et al.
- 1971
(Show Context)
Citation Context ...he unit ball of L∞/H∞. There is also a natural isometric isomorphism between L∞/H∞ and ¡ H10 ¢∗ . 2. Preliminaries We will need to make use of the following lemma of V. Adamjan, D. Arov, and M. Krein =-=[1]-=-. Lemma 1. Assume x is a vector in H2 satisfying kHfxk = kHfk kxk and set y = Hfx. Then kHfk−1 ¡ eity/x ¢ is unimodular on the unit circle. q = eity/x is the only function satisfying Hf = Hq and kqk∞ ... |

70 |
On bounded bilinear forms,”
- Nehari
- 1957
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Citation Context ...scussed here. We will use Hf to denote the Hankel operator with L∞ symbol f , given by Hf : H2 −→ ¡ H2 ¢⊥ , Hfh = (I − P ) fh where P is the orthogonal projection from L2 to H2. Nehari’s Theorem (see =-=[9]-=-) tells us that kHfk =distL∞ (f,H∞). This lets us see the set of Hankel operators Received by the editors September 19, 2001. 1991 Mathematics Subject Classification. Primary 47-B35, 47-B20. Key words... |

41 |
Harmonic Analysis of Operators on Hilbert Space,
- Nagy, Bercovici, et al.
- 2010
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Citation Context ...nto H (θ) , H∗ θw Hθw = T ∗ wH ∗ θ HθTw = w ∗(T )w(T ) where T is the model operator on H(θ), T = PH(θ)z|H(θ), and w(T ) is the functional calculus. The essential norm of w(T ) is given by (2.1), see =-=[8]-=-. 3. Subsets of Hankel Operators Now we prove the main theorem of this section and discuss some of its consequences. Theorem 1. If kHfk = 1 and there is an x in H2 with kHfxk = kHfk kxk, then Hf is an... |

23 | Hyponormality of Toeplitz operators,
- Cowen
- 1988
(Show Context)
Citation Context ...of the unit ball of the space of compact Hankel operators. 5. Cowen Sets We can use the Hankel operator methods to get several results concerning the extreme points of the reduced Cowen set (see [3], =-=[4]-=-) for a function f ∈ H∞. Recall that an operator A is hyponormal if its self-commutator [A∗, A] = A∗A−AA∗ is a positive operator. For a function f ∈ H∞, the Cowen set is Gf = {g ∈ H∞ : Tf+g is hyponor... |

8 | Hyponormal and subnormal Toeplitz operators, in Surveys of Some Recent Results - Cowen - 1988 |

7 |
Kernels of Hankel operators and hyponormality of Toeplitz operators
- Gu, Shapiro
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Citation Context ...t of Hankel operators. Proof. If kHfke < kHfk, then Hf attains its norm. Example: Consider the Hankel operators Hθz(1+αθ) for an inner function θ and complex constant α. It is shown by the authors in =-=[7]-=- that γ = °°°Hθz(1+αθ)°°° is given by γ2 = 2 + 2Re [αθ(0)] + |α|2 + q 4 |α|2 (1 + 2Re [αθ(0)]) + |α|4 − 4 |Im [αθ(0)]|2 2 . 4 CAIXING GU AND JONATHAN E. SHAPIRO If θ is rational, then Corollary 2 tell... |

2 |
Triangular Toeplitz contractions and Cowen sets for analytic polynomials
- Cho, Curto, et al.
- 2000
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Citation Context ...actions is strictly convex. We also find some extreme points in certain reduced Cowen sets and discuss cases in which they are or are not strictly convex. 1. Introduction M. Cho, R. Curto, and W. Lee =-=[2]-=- recently showed that the set TN of all lower triangular contractive Toeplitz matrices, matrices of the form c0 0 0 · · · 0 c1 c0 . . . ... ... . . . . . . . . . ... cN−2 . . . . . . 0 cN−1... |

2 |
Sensitivity minimization for arbitrary SISO distributed plants
- TANNENBAUM, ZAMES
- 1987
(Show Context)
Citation Context ...n the unit circle. q = eity/x is the only function satisfying Hf = Hq and kqk∞ = kHfk . For an inner function θ, let H (θ) = H2 ª θH2. The following lemma is from C. Foias, A. Tannenbaum and G. Zames =-=[6]-=-. For completeness, we outline a proof. Lemma 2. Let θ be an inner function and w be an analytic rational function, such that θ and w are coprime. The essential norm of Hθw is equal to max {|w(z)| : z... |