The object your method decompressGZIP() needs is a byte[].
So the basic, technical answer to the question you have asked is:
byte[] b = string.getBytes();
byte[] b = string.getBytes(Charset.forName("UTF-8"));
byte[] b = string.getBytes(StandardCharsets.UTF_8); // Java 7+ only
However, the problem you appear to be wrestling with is that this doesn't display very well. Calling toString() will just give you the default Object.toString() which is the class name + memory address. In your result [B@38ee9f13, the [B means byte[] and 38ee9f13 is the memory address, separated by an @.
For display purposes you can use:
Arrays.toString(bytes);
But this will just display as a sequence of comma-separated integers, which may or may not be what you want.
To get a readable String back from a byte[], use:
String string = new String(byte[] bytes, Charset charset);
The reason the Charset version is favored, is that all String objects in Java are stored internally as UTF-16. When converting to a byte[] you will get a different breakdown of bytes for the given glyphs of that String, depending upon the chosen charset.