# Two characterizations of automorphisms on B(X)

Studia Mathematica (1993)

- Volume: 105, Issue: 2, page 143-149
- ISSN: 0039-3223

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topŠemrl, Peter. "Two characterizations of automorphisms on B(X)." Studia Mathematica 105.2 (1993): 143-149. <http://eudml.org/doc/215990>.

@article{Šemrl1993,

abstract = {Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.},

author = {Šemrl, Peter},

journal = {Studia Mathematica},

keywords = {automorphisms on ; automorphism; surjective operators},

language = {eng},

number = {2},

pages = {143-149},

title = {Two characterizations of automorphisms on B(X)},

url = {http://eudml.org/doc/215990},

volume = {105},

year = {1993},

}

TY - JOUR

AU - Šemrl, Peter

TI - Two characterizations of automorphisms on B(X)

JO - Studia Mathematica

PY - 1993

VL - 105

IS - 2

SP - 143

EP - 149

AB - Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.

LA - eng

KW - automorphisms on ; automorphism; surjective operators

UR - http://eudml.org/doc/215990

ER -

## References

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