scholarly journals Spatial Numerical Range of Operators on Weighted Hardy Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Abdolaziz Abdollahi ◽  
Mohammad Taghi Heydari
Keyword(s):  
Hardy Spaces ◽  
Finite Rank ◽  
Numerical Range ◽  
Compact Operators ◽  
Weighted Hardy Spaces ◽  
Finite Rank Operators

We consider the spatial numerical range of operators on weighted Hardy spaces and give conditions for closedness of numerical range of compact operators. We also prove that the spatial numerical range of finite rank operators on weighted Hardy spaces is star shaped; though, in general, it does not need to be convex.

Dividing in the algebra of compact operators

2004 ◽  
Vol 69 (3) ◽  
pp. 817-829
Author(s):  
Alexander Berenstein
Keyword(s):  
Hilbert Space ◽  
Finite Rank ◽  
Compact Operators ◽  
Canonical Bases ◽  
Finite Rank Operators

Abstract.We interpret the algebra of finite rank operators as imaginaries inside a Hilbert space. We prove that the Hilbert space enlarged with these imaginaries has built-in canonical bases.

scholarly journals A remark on the slice map problem

1994 ◽  
Vol 17 (2) ◽  
pp. 401-404
Author(s):  
Muneo Chō ◽  
Tadasi Huruya
Keyword(s):  
Operator Algebra ◽  
Finite Rank ◽  
Closed Operator ◽  
Compact Operators ◽  
Finite Rank Operators ◽  
Weakly Closed ◽  
Fubini Product

It is shown that there exist aσ-weakly closed operator algebraA˜, generated by finite rank operators and aσ-weakly closed operator algebraB˜generated by compact operators such that the Fubini productA˜⊗¯FB˜contains properlyA˜⊗¯B˜.

scholarly journals Numerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces

2017 ◽  
Vol 25 (1) ◽  
pp. 87-98
Author(s):  
Mohammad Taghi Heydari
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Numerical Range ◽  
Linear Operators ◽  
Inner Product ◽  
Product Spaces ◽  
Weighted Hardy Space ◽  
Weighted Hardy Spaces ◽  
Bounded Linear ◽  
Inner Product Spaces

AbstractThe semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.

scholarly journals Toeplitz operators with PQC symbols on weighted Hardy spaces

1991 ◽  
Vol 97 (1) ◽  
pp. 194-214 ◽  
Author(s):  
Albrecht Böttcher ◽  
Ilya M Spitkovsky
Keyword(s):  
Hardy Spaces ◽  
Toeplitz Operators ◽  
Weighted Hardy Spaces
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