# Convergence of orthogonal series of projections in Banach spaces

Ryszard Jajte; Adam Paszkiewicz

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 137-153
- ISSN: 0066-2216

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topRyszard Jajte, and Adam Paszkiewicz. "Convergence of orthogonal series of projections in Banach spaces." Annales Polonici Mathematici 66.1 (1997): 137-153. <http://eudml.org/doc/269982>.

@article{RyszardJajte1997,

abstract = {For a sequence $(A_j)$ of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums $S_n = ∑^n_\{j=1\} A_j$ in a “strong” sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of $S_n$ (i.e. $S_\{n\}f → Af$ μ-a.e. for all f ∈ (A)).},

author = {Ryszard Jajte, Adam Paszkiewicz},

journal = {Annales Polonici Mathematici},

keywords = {idempotent; mutually orthogonal projections; L₂-space; convergence almost everywhere; -space; idempotent operators},

language = {eng},

number = {1},

pages = {137-153},

title = {Convergence of orthogonal series of projections in Banach spaces},

url = {http://eudml.org/doc/269982},

volume = {66},

year = {1997},

}

TY - JOUR

AU - Ryszard Jajte

AU - Adam Paszkiewicz

TI - Convergence of orthogonal series of projections in Banach spaces

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 137

EP - 153

AB - For a sequence $(A_j)$ of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums $S_n = ∑^n_{j=1} A_j$ in a “strong” sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of $S_n$ (i.e. $S_{n}f → Af$ μ-a.e. for all f ∈ (A)).

LA - eng

KW - idempotent; mutually orthogonal projections; L₂-space; convergence almost everywhere; -space; idempotent operators

UR - http://eudml.org/doc/269982

ER -

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