کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4591993 1335067 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Toeplitz operators associated to commuting row contractions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Toeplitz operators associated to commuting row contractions
چکیده انگلیسی

Let HH be a complex Hilbert space and let {Tn}n⩾1{Tn}n⩾1 be a sequence of commuting bounded operators on HH such that ∑n⩾1TnTn∗⩽IH. Let F(T¯) denote the space of all operators X   in B(H)B(H) for which ∑n⩾1TnXTn∗=X and suppose that F(T¯)≠{0}. We will show that there exists a triple {K,Γ,{Un}n⩾1}{K,Γ,{Un}n⩾1} where KK is a Hilbert space, Γ:K→HΓ:K→H is a bounded operator and {Un}n⩾1⊂B(K){Un}n⩾1⊂B(K) is a sequence of commuting normal operators with ∑n⩾1UnUn∗=IK such that TnΓ=ΓUnTnΓ=ΓUn for n⩾1n⩾1, and for which the mapping Y↦ΓYΓ∗Y↦ΓYΓ∗ is a complete isometry from the commutant of {Un}n⩾1{Un}n⩾1 onto the space F(T¯). Moreover we show that the inverse of this mapping can be extended to a ∗-homomorphismπ:C∗{IH,F(T¯)}→{Un}n⩾1′ from the unital C∗C∗-algebra generated by F(T¯) onto the commutant of {Un}n⩾1{Un}n⩾1. We also show that there exists a ∗-homomorphismΠ:C∗{IH,{Tn}n⩾1}→C∗{IK,{Un}n⩾1}Π:C∗{IH,{Tn}n⩾1}→C∗{IK,{Un}n⩾1} such that Π(Tn)=UnΠ(Tn)=Un for n⩾1n⩾1. In the particular case when {Tn}n⩾1{Tn}n⩾1 has only a finite number of non-zero components, it turns out that {Un}n⩾1{Un}n⩾1 is unitarily equivalent to the spherical unitary part of the standard commuting dilation of {Tn}n⩾1{Tn}n⩾1.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 254, Issue 6, 15 March 2008, Pages 1626–1641
نویسندگان
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