(1) The board of trustees may, in its corporate name:
(a) Contract and be contracted with, sue and be sued, and have and use a corporate seal, which it may alter at pleasure;
(b) Acquire, by itself or jointly with the city in which the library is located, by gift, purchase or otherwise, and hold, in the same manner, real and personal property to the use of the public library, for the purpose for which it is dedicated;
(c) Use, manage and improve, sell and convey, rent or lease property, and erect suitable buildings.
(2) The board of trustees may mortgage any real or personal property owned by the library to secure any sums borrowed for making repairs or improvements, or paying off any indebtedness it may owe. The mortgage shall not exceed $1,000,000.