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- Dilation_(operator_theory) abstract "In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the orthogonal projection onto H is T.More formally, let T be a bounded operator on some Hilbert space H, and H be a subspace of a larger Hilbert space H' . A bounded operator V on H' is a dilation of T ifwhere is projection on H.V is said to be a unitary dilation (respectively, normal, isometric, etc.) if V is unitary (respectively, normal, isometric, etc.). T is said to be a compression of V. If an operator T has a spectral set , we say that V is a normal boundary dilation or a normal dilation if V is a normal dilation of T and .Some texts impose an additional condition. Namely, that a dilation satisfy the following (calculus) property:where f(T) is some specified functional calculus (for example, the polynomial or H∞ calculus). The utility of a dilation is that it allows the "lifting" of objects associated to T to the level of V, where the lifted objects may have nicer properties. See, for example, the commutant lifting theorem.".
- Dilation_(operator_theory) wikiPageID "3319942".
- Dilation_(operator_theory) wikiPageRevisionID "598446370".
- Dilation_(operator_theory) hasPhotoCollection Dilation_(operator_theory).
- Dilation_(operator_theory) subject Category:Operator_theory.
- Dilation_(operator_theory) subject Category:Unitary_operators.
- Dilation_(operator_theory) type Abstraction100002137.
- Dilation_(operator_theory) type Function113783816.
- Dilation_(operator_theory) type MathematicalRelation113783581.
- Dilation_(operator_theory) type Operator113786413.
- Dilation_(operator_theory) type Relation100031921.
- Dilation_(operator_theory) type UnitaryOperators.
- Dilation_(operator_theory) comment "In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the orthogonal projection onto H is T.More formally, let T be a bounded operator on some Hilbert space H, and H be a subspace of a larger Hilbert space H' .".
- Dilation_(operator_theory) label "Dilation (operator theory)".
- Dilation_(operator_theory) label "伸張 (作用素論)".
- Dilation_(operator_theory) sameAs 伸張_(作用素論).
- Dilation_(operator_theory) sameAs m.095ltv.
- Dilation_(operator_theory) sameAs Q5276677.
- Dilation_(operator_theory) sameAs Q5276677.
- Dilation_(operator_theory) sameAs Dilation_(operator_theory).
- Dilation_(operator_theory) wasDerivedFrom Dilation_(operator_theory)?oldid=598446370.
- Dilation_(operator_theory) isPrimaryTopicOf Dilation_(operator_theory).