The Minimal Normal Extension for M z on the Hardy Space of a Planar Region

1990 ◽  
Vol 318 (1) ◽  
pp. 57
Author(s):  
John Spraker
Keyword(s):  
Hardy Space ◽  
Normal Extension ◽  
Planar Region ◽  
Minimal Normal Extension

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.).

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.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

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