scholarly journals A Generalization of the Subspace Theorem With Polynomials of Higher Degree

2008 ◽  
pp. 175-198 ◽  
Author(s):  
Jan-Hendrik Evertse ◽  
Roberto G. Ferretti
Keyword(s):  
Subspace Theorem

A note on some applications of the subspace theorem

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Rishabh Agnihotri ◽  
Debasish Karmakar ◽  
Veekesh Kumar
Keyword(s):  
Subspace Theorem

scholarly journals An invariant subspace theorem on subdecomposable operators

2000 ◽  
Vol 61 (1) ◽  
pp. 11-26
Author(s):  
Mingxue Liu
Keyword(s):  
Invariant Subspace ◽  
Additional Condition ◽  
Subspace Theorem ◽  
Subspace Problem ◽  
Invariant Subspace Problem

H. Mohebi and M. Radjabalipour raised a conjecture on the invariant subspace problem in 1994. In this paper, we prove the conjecture under an additional condition, and obtain an invariant subspace theorem on subdecomposable operators.

Schmidt’s subspace theorem for non-subdegenerate families of hyperplanes

2021 ◽  
pp. 1-18
Author(s):  
Duc Hiep Pham
Keyword(s):  
Type Theorem ◽  
Exceptional Sets ◽  
Subspace Theorem ◽  
Lang's Conjecture ◽  
Lang’S Conjecture

In this paper, we establish a Schmidt’s subspace theorem for non-subdegenerate families of hyperplanes. In particular, our result improves the previous result on Schmidt’s subspace type theorem for the case of non-degenerate families of hyperplanes, and furthermore, also shows the sharpness of the condition of non-subdegeneracy. As a consequence, we deduce a version of Lang’s conjecture on exceptional sets in the case of complements of hyperplanes.

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.

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