Page 1. 1984] NOTES 127 which reduces to Tan 0 = zo. But Tan 0 is also y/x so that y = zox. Now s... more Page 1. 1984] NOTES 127 which reduces to Tan 0 = zo. But Tan 0 is also y/x so that y = zox. Now substitution of these values z = zo and y = zox changes the equation of the surface (2) to ZOX3 + z3x3 + z3X - 2zOx2-2z3x2 + 2zox - zox = 0; separating and factoring ...
Journal für die reine und angewandte Mathematik (Crelles Journal), 1977
Page 1. Limagons, normal operators and polar factorizations By Robert F. Olin and James E. Thomso... more Page 1. Limagons, normal operators and polar factorizations By Robert F. Olin and James E. Thomson at Blacksburg I. Introduction and preliminaries Throughout this paper 7V will be a normal operator on a separable infinite dimensional Hubert space. ...
Transactions of the American Mathematical Society, 1982
We use the notion of generalized Toeplitz operators to obtain some basic results concerning the C... more We use the notion of generalized Toeplitz operators to obtain some basic results concerning the C ∗ {C^{\ast }} -algebra generated by a subnormal operator. We apply these results to problems concerning the intersection of C ∗ ( S ) {C^{\ast }}(S) with rationally closed algebras generated by S S . In particular, we prove that C ∗ ( S ) ∩ W ( S ) = { f ( S ) : f ∈ R ( σ W ( S ) ( S ) ) } {C^{\ast }}(S) \cap \mathcal {W}(S) = \{ f(S):f \in R({\sigma _{\mathcal {W}(S)}}(S))\} . The spectral inclusion property for generalized Toeplitz operators with symbols in P ∞ ( μ ) + C ( σ ( N ) ) {P^\infty }(\mu ) + C(\sigma (N)) is also considered.
Memoirs of the American Mathematical Society, 1986
... Some of the results in Sections 2 and 3 appear in the first author's Ph.D thesis written... more ... Some of the results in Sections 2 and 3 appear in the first author's Ph.D thesis written under the supervision of Robert Olin. o The last two authors were partially supported by a grant from the National Science Foundation during the preparation of this paper. Page 10. ...
Page 1. JOURNAL OF FUNCTIONAL ANALYSIS 134, 297 320 (1995) The Commutant of Multiplication by z o... more Page 1. JOURNAL OF FUNCTIONAL ANALYSIS 134, 297 320 (1995) The Commutant of Multiplication by z on the Closure of Polynomials in Zf(/y) Robert F. Olin* Department ofMathematics, Virginia Tech, Bktckshurg, Virginia ...
Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q... more Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q 1986 Birkhauser Verlag, Basel CELLULAR-INDECOMPOSABLE SU6tlORI'~L OPERATORS II Robert F. Olin I) and James E. Thomson I) ...
Page 1. Integral Equations and Operator Theory Vol. 7 (1984) 0378-620X/84/030392-3951.50+0.20/0 9... more Page 1. Integral Equations and Operator Theory Vol. 7 (1984) 0378-620X/84/030392-3951.50+0.20/0 9 1984 Birkh[user Verlag, Basel CELLULAR-INDECOMPOSABLE SUBNORMAL OPERATORS Robert F. Olin* and James E. Thomson* ...
It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric w... more It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.
Let S be a subnormal operator on a Hilbert space ℋ and let N be its minimal normal extension on t... more Let S be a subnormal operator on a Hilbert space ℋ and let N be its minimal normal extension on the Hilbert space ℋ. (We refer the reader to [5, 15] for the basic material on subnormal operators.) Denote the commutant and double commutant of an operator T by ﹛T﹜’ and ﹛T﹜”, respectively.
Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q... more Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q 1986 Birkhauser Verlag, Basel CELLULAR-INDECOMPOSABLE SU6tlORI'~L OPERATORS II Robert F. Olin I) and James E. Thomson I) ...
Page 1. 1984] NOTES 127 which reduces to Tan 0 = zo. But Tan 0 is also y/x so that y = zox. Now s... more Page 1. 1984] NOTES 127 which reduces to Tan 0 = zo. But Tan 0 is also y/x so that y = zox. Now substitution of these values z = zo and y = zox changes the equation of the surface (2) to ZOX3 + z3x3 + z3X - 2zOx2-2z3x2 + 2zox - zox = 0; separating and factoring ...
Journal für die reine und angewandte Mathematik (Crelles Journal), 1977
Page 1. Limagons, normal operators and polar factorizations By Robert F. Olin and James E. Thomso... more Page 1. Limagons, normal operators and polar factorizations By Robert F. Olin and James E. Thomson at Blacksburg I. Introduction and preliminaries Throughout this paper 7V will be a normal operator on a separable infinite dimensional Hubert space. ...
Transactions of the American Mathematical Society, 1982
We use the notion of generalized Toeplitz operators to obtain some basic results concerning the C... more We use the notion of generalized Toeplitz operators to obtain some basic results concerning the C ∗ {C^{\ast }} -algebra generated by a subnormal operator. We apply these results to problems concerning the intersection of C ∗ ( S ) {C^{\ast }}(S) with rationally closed algebras generated by S S . In particular, we prove that C ∗ ( S ) ∩ W ( S ) = { f ( S ) : f ∈ R ( σ W ( S ) ( S ) ) } {C^{\ast }}(S) \cap \mathcal {W}(S) = \{ f(S):f \in R({\sigma _{\mathcal {W}(S)}}(S))\} . The spectral inclusion property for generalized Toeplitz operators with symbols in P ∞ ( μ ) + C ( σ ( N ) ) {P^\infty }(\mu ) + C(\sigma (N)) is also considered.
Memoirs of the American Mathematical Society, 1986
... Some of the results in Sections 2 and 3 appear in the first author's Ph.D thesis written... more ... Some of the results in Sections 2 and 3 appear in the first author's Ph.D thesis written under the supervision of Robert Olin. o The last two authors were partially supported by a grant from the National Science Foundation during the preparation of this paper. Page 10. ...
Page 1. JOURNAL OF FUNCTIONAL ANALYSIS 134, 297 320 (1995) The Commutant of Multiplication by z o... more Page 1. JOURNAL OF FUNCTIONAL ANALYSIS 134, 297 320 (1995) The Commutant of Multiplication by z on the Closure of Polynomials in Zf(/y) Robert F. Olin* Department ofMathematics, Virginia Tech, Bktckshurg, Virginia ...
Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q... more Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q 1986 Birkhauser Verlag, Basel CELLULAR-INDECOMPOSABLE SU6tlORI'~L OPERATORS II Robert F. Olin I) and James E. Thomson I) ...
Page 1. Integral Equations and Operator Theory Vol. 7 (1984) 0378-620X/84/030392-3951.50+0.20/0 9... more Page 1. Integral Equations and Operator Theory Vol. 7 (1984) 0378-620X/84/030392-3951.50+0.20/0 9 1984 Birkh[user Verlag, Basel CELLULAR-INDECOMPOSABLE SUBNORMAL OPERATORS Robert F. Olin* and James E. Thomson* ...
It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric w... more It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.
Let S be a subnormal operator on a Hilbert space ℋ and let N be its minimal normal extension on t... more Let S be a subnormal operator on a Hilbert space ℋ and let N be its minimal normal extension on the Hilbert space ℋ. (We refer the reader to [5, 15] for the basic material on subnormal operators.) Denote the commutant and double commutant of an operator T by ﹛T﹜’ and ﹛T﹜”, respectively.
Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q... more Page 1. Integral Equations and Operator Theory Vol. 9 (1986) 0378-620X/86/040600-I0~1.50+0.20/0 Q 1986 Birkhauser Verlag, Basel CELLULAR-INDECOMPOSABLE SU6tlORI'~L OPERATORS II Robert F. Olin I) and James E. Thomson I) ...
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