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21 results on '"Normal operator"'

3. Invariant Subspaces for Some Compact Perturbations of Normal Operators

Author

Liu, Mingxue, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Wang, Fu Lee, editor, Gong, Zhiguo, editor, Luo, Xiangfeng, editor, and Lei, Jingsheng, editor

Published
2010
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8. Theorems on normal operators and on related canonical mapping

Author

Nikodým, Otton Martin, Doob, J. L., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Mumford, D., editor, Schmidt, F. K., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, and Nikodým, Otton Martin

Published
1966
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9. Maximal normal operator and its canonical representation

Author

Nikodým, Otton Martin, Doob, J. L., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Mumford, D., editor, Schmidt, F. K., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, and Nikodým, Otton Martin

Published
1966
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13. 10 Multiplicative Representations of Resolvents

Author

Michael Gil

Subjects
Algebra, Pure mathematics, Operator (computer programming), Spectral representation, Product (mathematics), Multiplicative function, Normal operator, Identity (music), Mathematics, Resolvent, Resolution (algebra)
Abstract

In the present chapter we introduce the notion of the multiplicative operator integral in a separable Hilbert space H. By virtue of the multiplicative operator integral, we derive spectral representations for resolvents of various classes of P-triangular operators. These representations are generalizations of the classical spectral representation for the resolvent of a normal operator. If the maximal resolution of the identity is discrete, then the multiplicative integral is an operator product.

Published
2003

14. Normal Cones to Sublevel Sets: An Axiomatic Approach

Author

Aris Daniilidis and Didier Aussel

Subjects
Quasiconvex function, Pure mathematics, Pseudoconvexity, Axiomatic system, Equivalence relation, Normal operator, Subderivative, Mathematics
Abstract

An axiomatic approach of normal operators to sublevel sets is given. Considering the Clarke-Rockafellar subdifferential (resp. quasiconvex functions), the definition given in [4] (resp. [5]) is recovered. Moreover, the results obtained in [4] are extended in this more general setting. Under mild assumptions, quasiconvex continuous functions are classified, establishing an equivalence relation between functions with the same normal operator. Applications in pseudoconvexity are also discussed.

Published
2001

15. Close to normal operators

Author

John B. Conway

Subjects
symbols.namesake, Pure mathematics, symbols, Hilbert space, Normal operator, Harmonic measure, Jordan curve theorem, Mathematics, Functional calculus
Published
1994

17. Operators $$N{f^ \cdot }\left( {\mathop {{\text{ }}x}\limits^ \cdot } \right){ = _{df}}\varphi \left( x \right) \cdot \mathop {{\text{ }}f}\limits^ \cdot \left( {\mathop {{\text{ }}x}\limits^ \cdot } \right)$$ for ordinary functions f

Author

Otton Martin Nikodým

Subjects
Discrete mathematics, Operational calculus, Generalization, Canonical form, Normal operator, Term (logic), Mathematics
Abstract

The purpose of this Chapter [J.] is to supply preparations for a new theory of functions F(N),where N is a normal operator. These functions are not ordinary compound functions, but they must be conceived as a suitable generalization of iterations of N,viz. N2 = N N, N3 = N N2 etc. Therefore the term “operational calculus” used by Stone (26) seems adequate.

Published
1966

19. Maximal normal operator and its canonical representation

Author

Otton Martin Nikodým

Subjects
Pure mathematics, Mathematics::Operator Algebras, Generalization, Mathematical analysis, Normal operator, Canonical form, Mathematics::Spectral Theory, Shift operator, Unitary state, Hermitian matrix, Eigenvalues and eigenvectors, Mathematics, Quasinormal operator
Abstract

Maximal normal operators1 constitute a generalization of selfadjoint (hermitian) operations. Vagely speaking they may be conceived as operators with mutually orthogonal eigenvectors, but with complex eigenvalues. Selfadjoint operators and unitary operators are particular cases of maximal normal operators.

Published
1966

20. Transformation of strong Kernels

Author

György I. Targonski

Subjects
Pure mathematics, symbols.namesake, Complex conjugate, Transformation (function), Hilbert space, symbols, Normal operator, Mathematics, Bounded operator
Published
1967

21. Multiplicity of spectrum of maximal normal operators

Author

Otton Martin Nikodým

Subjects
Pure mathematics, Operator (computer programming), Continuous spectrum, Mathematical analysis, Multiplicity (mathematics), Normal operator, Eigenvalues and eigenvectors, Mathematics
Abstract

If the normal operator has discontinuous spectrum, the multiplicity of an eigenvalue is easy to define. The case of continuous spectrum is more difficult, but the canonical multiplane-representation of the operator will be helpful. Our theory will define the multiplicity so that it will be not only precise, but intuitionally simple and even visual. We start with some hypotheses and preliminaries.

Published
1966

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