scholarly journals Functional relationships between a subnormal operator and its minimal normal extension

1976 ◽  
Vol 63 (1) ◽  
pp. 221-229 ◽  
Author(s):  
Robert Olin
Keyword(s):  
Subnormal Operator ◽  
Normal Extension ◽  
Functional Relationships ◽  
Minimal Normal Extension

Lifting the Commutant of a Subnormal Operator

1979 ◽  
Vol 31 (1) ◽  
pp. 148-156 ◽  
Author(s):  
Robert F. Olin ◽  
James E. Thomson
Keyword(s):  
Hilbert Space ◽  
Subnormal Operator ◽  
Basic Material ◽  
Normal Extension ◽  
Subnormal Operators ◽  
Double Commutant ◽  
Minimal Normal Extension

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.

scholarly journals The spectrum of orthogonal sums of subnormal pairs

1988 ◽  
Vol 30 (1) ◽  
pp. 11-15 ◽  
Author(s):  
K. Rudol
Keyword(s):  
Invariant Subspace ◽  
Spectral Theory ◽  
Existence And Uniqueness ◽  
Normal Extension ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Basic Properties ◽  
Subspace Theorem ◽  
Subnormal Operators ◽  
Minimal Normal Extension

This note provides yet another example of the difficulties that arise when one wants to extend the spectral theory of subnormal operators to subnormal tuples. Several basic properties of a subnormal operator Y remain true for tuples; e.g. the existence and uniqueness of its minimal normal extension N, the spectral inclusion σ(N)⊂ σ(Y)-proved for n-tuples in [4] and generalized to infinite tuples in [5]. However, neither the invariant subspace theorem nor the spectral mapping theorem in the “strong form” as in [3] is known so far for subnormal tuples.

Spectral Inclusion and C.N.E.

1982 ◽  
Vol 34 (4) ◽  
pp. 883-887 ◽  
Author(s):  
A. R. Lubin
Keyword(s):  
Hilbert Space ◽  
Linear Operators ◽  
Normal Extension ◽  
Unitary Equivalence ◽  
Bounded Linear ◽  
Multi Index ◽  
Reducing Subspace ◽  
Normal Operators ◽  
Image Position ◽  
Minimal Normal Extension

1. An n-tuple S = (S1, …, Sn) of commuting bounded linear operators on a Hilbert space H is said to have commuting normal extension if and only if there exists an n-tuple N = (N1, …, Nn) of commuting normal operators on some larger Hilbert space K ⊃ H with the restrictions Ni|H = Si, i = 1, …, n. If we takethe minimal reducing subspace of N containing H, then N is unique up to unitary equivalence and is called the c.n.e. of S. (Here J denotes the multi-index (j1, …, jn) of nonnegative integers and N*J = N1*jl … Nn*jn and we emphasize that c.n.e. denotes minimal commuting normal extension.) If n = 1, then S1 = S is called subnormal and N1 = N its minimal normal extension (m.n.e.).

Three-dimensional organization and functional relationships of endocytotic compartments in pig intestinal epithelial cells

1992 ◽  
Vol 50 (1) ◽  
pp. 576-577
Author(s):  
Julian P. Heath ◽  
Buford L. Nichols ◽  
László G. Kömüves
Keyword(s):  
Electron Microscopy ◽  
Epithelial Cells ◽  
Intestinal Epithelial Cells ◽  
Three Dimensional ◽  
Intestinal Epithelial ◽  
Cell Surfaces ◽  
Basal Surface ◽  
Functional Relationships

The newborn pig intestine is adapted for the rapid and efficient absorption of nutrients from colostrum. In enterocytes, colostral proteins are taken up into an apical endocytotic complex of channels that transports them to target organelles or to the basal surface for release into the circulation. The apical endocytotic complex of tubules and vesicles clearly is a major intersection in the routes taken by vesicles trafficking to and from the Golgi, lysosomes, and the apical and basolateral cell surfaces.Jejunal tissues were taken from piglets suckled for up to 6 hours and prepared for electron microscopy and immunocytochemistry as previously described.

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