Year: 2025
Type: article
Abstract: It was a remarkable result of the last decades that every Banach space operator has an almost invariant half-space; see [1] and [17]. Refining the technique used in [1], it has been shown quite recently that every operator $$T$$ T on a complex Hilbert space $$\mathcal{H}$$ H has a diagonal operator inside itself; see [9]. Applying this result to a block-triangular operator $$T\in\mathcal{L}(\mathcal{H}_1 \oplus \mathcal{H}_2)$$ T ∈ L ( H 1 ⊕ H 2 ) , it can be proved that a translate of $$T$$ T is similar to an operator $$\widehat{T}\in\mathcal{L}(\mathcal{H}^{(4)})$$ T ^ ∈ L ( H ( 4 ) ) with two diagonal entries $$D$$ D , $$D_{*} $$ D ∗ and two entries $$F$$ F , $$F _{*} $$ F ∗ of rank $$1$$ 1 . Given any operator $$Q= [Q_{i,j}]_4$$ Q = [ Q i , j ] 4 in the commutant $$\{\widehat{T}\}'$$ { T ^ } ′ of $$\widehat{T}$$ T ^ , the operator entry $$Q_{4,1}$$
Source: Analysis Mathematica
Author: L. Kérchy
Institution: University of Szeged
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4416203290