Duality in spaces of polynomials of degree at most n

作者：Boyd Christopher^*; Brown Anthony

来源：Journal of Mathematical Analysis and Applications, 2015, 429(2): 1271-1290.

DOI：10.1016/j.jmaa.2015.04.055

• Polynomials
• Sums of spaces of tensor products
• Integral nuclear duality

We study spaces of continuous polynomials of degree at most n between Banach spaces. Using symmetric tensor products we show that any polynomial of degree at most n has a natural linearisation and that the space of all scalar-valued polynomials of degree at most n has an isometric predual. We introduce the spaces of integral and nuclear polynomials of degree at most n and endow them with norms that allows us to develop a duality theory for spaces of polynomials of degree at most n.

• 出版日期2015-9-15