Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces
Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces
Abstract We obtain several extensions of a theorem of Shevchik which asserts that if R is a proper dense operator range in a separable Banach space E , then there exists a compact, one-to-one and dense-range operator $$T:E\rightarrow E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>:</mml:mo> <mml:mi>E</mml:mi> <mml:mo>→</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> such …