Spectrum-preserving maps on Banach Algebras

This book looks at the so-called Kaplansky's problem, a linear preserver problem concerned with maps that preserve properties related to invertibility. In this book, we have given a detailed exploration of the so-called Kaplansky's problem in which four different results (or rather answers) have been documented. None of these results answers the question in totality. The answers are a mere motivation for our continued search for an eventual solution.